40 pages ; 22 cm

Topics: Number theory, Galois theory, Galois theory, Number theory

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3.0

Apr 25, 2022
04/22

by
Adams, J. Frank (John Frank)

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x, 373 p. ; 21 cm

Topics: Homotopy theory, Homology theory, Cobordism theory

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5.0

Jul 23, 2021
07/21

by
Puschnigg, Michael, 1959-

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xxiii, 238 p. ; 24 cm

Topics: Homology theory, K-theory, KK-theory, Index theory (Mathematics)

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8.0

Jun 30, 2018
06/18

by
Ori Parzanchevski; Peter Sarnak

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To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of optimal strong approximation for integral quadratic forms associated with certain special quaternion algebras and their arithmetic groups. The generators give super efficient 1-qubit quantum gates and are natural building blocks for the design of universal...

Topics: Group Theory, Spectral Theory, Number Theory, Mathematics

Source: http://arxiv.org/abs/1704.02106

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6.0

Jun 30, 2018
06/18

by
Anton Lyubinin

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The topic of this paper is a generalization of Tannaka duality to coclosed categories. As an application we prove reconstruction theorems for coalgebras (and bialgebras) in categories of topological vector spaces over a nonarchimedean field K. In particular, our results imply reconstruction and recognition theorems for categories of locally analytic representations of compact $p$-adic groups. Also, as an example, we discuss a certain (trivial) extension of the geometric Satake correspondence.

Topics: Mathematics, Category Theory, Number Theory, Representation Theory

Source: http://arxiv.org/abs/1411.3183

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Jun 26, 2018
06/18

by
Dipendra Prasad

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These are the notes for some lectures given by this author at Harish-Chandra Research Institute, Allahabad in March 2014 for a workshop on Schur multipliers. The lectures aimed at giving an overview of the subject with emphasis on groups of Lie type over finite, real and $p$-adic fields.

Topics: Mathematics, Representation Theory, Number Theory, Group Theory

Source: http://arxiv.org/abs/1502.02140

v, 104 p. 21 cm

Topics: Equations, Theory of, Galois theory, Group theory

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Jun 30, 2018
06/18

by
Robert Guralnick; Florian Herzig; Pham Huu Tiep

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The notion of adequate subgroups was introduced by Jack Thorne [59]. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown in [22] and [23] that if the dimension is smaller than the characteristic then almost all absolutely irreducible representations are adequate. We extend the results by considering all...

Topics: Mathematics, Number Theory, Representation Theory, Group Theory

Source: http://arxiv.org/abs/1405.0043

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8.0

Jun 30, 2018
06/18

by
Toshiyuki Kobayashi

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For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of $dim Sh(\lambda, \nu)$ is also obtained. Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible...

Topics: Mathematics, Number Theory, Representation Theory, Group Theory

Source: http://arxiv.org/abs/1401.0117

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Jun 28, 2018
06/18

by
Supriya Pisolkar; C. S. Rajan

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Let $G$ be a connected, absolutely almost simple, algebraic group defined over a finitely generated, infinite field $K$, and let $\Gamma$ be a Zariski dense subgroup of $G(K)$. We show, apart from some few exceptions, that the commensurability class of the field $\mathcal{F}$ given by the compositum of the splitting fields of characteristic polynomials of generic elements of $\Gamma$ determines the group $G$ upto isogeny over the algebraic closure of $K$.

Topics: Group Theory, Number Theory, Mathematics, Spectral Theory

Source: http://arxiv.org/abs/1508.01348

iv, 283 p. : 24 cm

Topics: Equations, Theory of, Galois theory, Group theory

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Jun 27, 2018
06/18

by
Tobias Finis; Erez Lapid

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This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.

Topics: Spectral Theory, Representation Theory, Mathematics, Number Theory

Source: http://arxiv.org/abs/1504.04795

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2.0

Jun 29, 2018
06/18

by
Jesús Ibarra; Alberto G. Raggi-Cárdenas; Nadia Romero

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Let $R$ be a commutative unital ring. We construct a category $\mathcal{C}_R$ of fractions $X/G$, where $G$ is a finite group and $X$ is a finite $G$-set, and with morphisms given by $R$-linear combinations of spans of bisets. This category is an additive, symmetric monoidal and self-dual category, with a Krull-Schmidt decomposition for objects. We show that $\mathcal{C}_R$ is equivalent to the additive completion of the biset category and that the category of biset functors over $R$ is...

Topics: Category Theory, Group Theory, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1610.00808

pte. 1. Teoria dei gruppi di sostituzioni -- pte. 2. Teoria delle equazioni algebriche secondo Galois

Topics: Group theory, Equations, Theory of, Galois theory

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5.0

Jun 28, 2018
06/18

by
Frank Lübeck; Robert Guralnick; Jun Yu

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We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and so also over Q. We show that these triples give rise to rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic 0.

Topics: Group Theory, Representation Theory, Number Theory, Mathematics

Source: http://arxiv.org/abs/1511.06871

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4.0

Jun 30, 2018
06/18

by
Yury A. Neretin

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We extend the Weil representation of infinite-dimensional symplectic group to a representation a certain category of linear relations.

Topics: Group Theory, Category Theory, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1703.07238

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5.0

Jun 30, 2018
06/18

by
Georg Tamme

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We prove a comparison theorem between locally analytic group cohomology and Lie algebra cohomology for locally analytic representations of a Lie group over a nonarchimedean field of characteristic 0. The proof is similar to that of van-Est's isomorphism and uses only a minimum of functional analysis.

Topics: Mathematics, Number Theory, Representation Theory, Group Theory

Source: http://arxiv.org/abs/1408.4301

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Jun 26, 2018
06/18

by
Wei Wang

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To $2$-categorify the theory of group representations, we introduce the notions of the $3$-representation of a group in a strict $3$-category and the strict $2$-categorical action of a group on a strict $2$-category. We also $2$-categorify the concept of the trace by introducing the $2$-categorical trace of a $1$-endomorphism in a strict $3$-category. For a $3$-representation $\rho$ of a group $G$ and an element $f$ of $G$, the $2$-categorical trace $\mathbb{T}r_2 \rho_f $ is a category....

Topics: Category Theory, Mathematics, Representation Theory, Group Theory

Source: http://arxiv.org/abs/1502.04191

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0.0

May 19, 2022
05/22

by
Baggeroer, Arthur B

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xii, 198 p. 24 cm

Topics: Signal theory (Telecommunication), Estimation theory, Control theory

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4.0

Jun 30, 2018
06/18

by
Ashvin Swaminathan

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The action of the absolute Galois group $\text{Gal}(K^{\text{ksep}}/K)$ of a global field $K$ on a tree $T(\phi, \alpha)$ of iterated preimages of $\alpha \in \mathbb{P}^1(K)$ under $\phi \in K(x)$ with $\text{deg}(\phi) \geq 2$ induces a homomorphism $\rho: \text{Gal}(K^{\text{ksep}}/K) \to \text{Aut}(T(\phi, \alpha))$, which is called an arboreal Galois representation. In this paper, we address a number of questions posed by Jones and Manes about the size of the group $G(\phi,\alpha) :=...

Topics: Mathematics, Number Theory, Representation Theory, Group Theory

Source: http://arxiv.org/abs/1407.7012

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Jun 29, 2018
06/18

by
Aaron Landesman; Ashvin Swaminathan; James Tao; Yujie Xu

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For a positive integer $g$, let $\mathrm{Sp}_{2g}(R)$ denote the group of $2g \times 2g$ symplectic matrices over a ring $R$. Assume $g \ge 2$. For a prime number $\ell$, we give a self-contained proof that any closed subgroup of $\mathrm{Sp}_{2g}(\mathbb{Z}_\ell)$ which surjects onto $\mathrm{Sp}_{2g}(\mathbb{Z}/\ell\mathbb{Z})$ must in fact equal all of $\mathrm{Sp}_{2g}(\mathbb{Z}_\ell)$. The result and the method of proof are both motivated by group-theoretic considerations that arise in...

Topics: Number Theory, Group Theory, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1607.04698

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Jun 29, 2018
06/18

by
Gaëtan Chenevier

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As is well-known, the compact groups Spin(7) and SO(7) both have a single conjugacy class of compact subgroups of exceptional type G_2. We first show that if H is a subgroup of Spin(7), and if each element of H is conjugate to some element of G_2, then H itself is conjugate to a subgroup of G_2. The analogous statement for SO(7) turns out be false, and our main result is a classification of all the exceptions. They are the following groups, embedded in each case in SO(7) in a very specific way:...

Topics: Number Theory, Group Theory, Representation Theory, Mathematics

Source: http://arxiv.org/abs/1606.02991

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Jun 28, 2018
06/18

by
Duong Hoang Dung

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We present a conjectured formula for the representation zeta function of the Heisenberg group over $\mathcal{O}[x]/(x^n)$ where $\mathcal{O}$ is the ring of integers of some number field. We confirm the conjecture for $n\leq 3$ and raise several questions.

Topics: Group Theory, Number Theory, Mathematics, Representation Theory

Source: http://arxiv.org/abs/1508.03507

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7.0

Aug 26, 2021
08/21

by
McEliece, Robert J

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xvi, 302 p. : 24 cm

Topics: Information theory, Coding theory

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718

Jan 26, 2009
01/09

by
Barnett, S. J. ( Samuel Jackson), 1873-1956

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Book digitized by Google from the library of University of Michigan and uploaded to the Internet Archive by user tpb.

Topics: Electromagnetic theory, Electromagnetic theory

Source: http://books.google.com/books?id=oaE3AAAAMAAJ&oe=UTF-8

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Jul 17, 2019
07/19

by
Anderson, Kenneth W

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191 p. 23 cm

Topics: Functor theory, Set theory

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631

Sep 13, 2008
09/08

by
Lejeune Dirichlet, Peter Gustav, 1805-1859

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Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

Topics: Number theory, Number theory

Source: http://books.google.com/books?id=-3Q4AAAAMAAJ&oe=UTF-8

Bibliography: p. 16

Topics: Graph theory, Ramsey theory

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3.0

Dec 22, 2021
12/21

by
Schmidt, Roland, 1944-

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xv, 572 p. : 25 cm

Topics: Group theory, Lattice theory

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132

Jul 27, 2017
07/17

by
Higgins, William, 1763-1825. no 91009637

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3 unnumbered leaves, 180 pages : (8vo)

Topics: Atomic theory, Atomic theory

University of Illinois Urbana-Champaign

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157

May 1, 2013
05/13

by
Wei, W. D; Liu, C. L. (Chung Laung), 1934- author; University of Illinois at Urbana-Champaign. Department of Computer Science

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"UIUCDCS-R-81-1050"

Topics: Graph theory, Ramsey theory

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399

Sep 10, 2008
09/08

by
Bachmann, Paul, 1837-1920

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: Number theory, Number theory

Source: http://books.google.com/books?id=uysCAAAAYAAJ&oe=UTF-8

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Oct 7, 2021
10/21

by
Goldie, Charles M

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xiv, 210 p. : 24 cm

Topics: Coding theory, Information theory

ix, 211, [1] pages 19 cm

Topics: Set theory, Set theory

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44

Jan 15, 2018
01/18

by
Daniel Ellsberg

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Abstract of PhD Thesis Risk Ambiguity and Decision.

Topics: decision theory, game theory

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27

Jan 15, 2018
01/18

by
Daniel Ellsberg

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Draft notes taken during the writing of thesis Risk, Ambiguity, and Decision.

Topics: decision theory, game theory

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49

Jan 16, 2018
01/18

by
Daniel Ellsberg

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Paper on Decision Theory. unknown

Topics: decision theory, game theory

Vita

Topics: Graph theory, Machine theory

862
862

Aug 12, 2009
08/09

by
Bianchi, Luigi, 1856-1928; Boccara, Vittorio, 1871- ed

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: Group theory, Galois theory

Source: http://books.google.com/books?id=NqcKAAAAYAAJ&oe=UTF-8

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May 7, 2021
05/21

by
Karg-Elert, Sigfrid; Karg-Elert, Sigfrid, 1877-1933

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2 volumes in 3 : 25 cm

Topics: Music theory, Music theory

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Dec 4, 2019
12/19

by
Kogan, Jacob, 1954-

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viii, 106 p. ; 25 cm

Topics: Control theory, Bifurcation theory

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33

Jan 15, 2018
01/18

by
Daniel Ellsberg

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Appendix of PhD Thesis Risk, Ambiguity, and Decision.

Topics: decision theory, game theory

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50

Jan 13, 2018
01/18

by
Daniel Ellsberg

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Original thesis submitted to the Harvard Economics department. A groundbreaking work in Decision Theory.

Topics: decision theory, game theory

[65]-143 p. ; 30 cm

Topics: Group theory, Galois theory

We construct binary de Bruijn graphs of odd order using recursive generation. We also explore the properties and nuances of these particular graphs. The recursive method developed for this thesis could in principle be used for other de Bruijn graphs of a different order. Suggestions on how this is accomplished are included in the paper and areas of further research topics.

Topics: Graph theory, Recursion theory

California Digital Library

1,722
1.7K

Feb 28, 2007
02/07

by
Dickson, Leonard E. (Leonard Eugene), 1874-

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Includes bibliographical references and index

Topics: Group theory, Galois theory

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162

Jan 15, 2018
01/18

by
Daniel Ellsberg

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Research notes on decision theory, research conducted during writing of PhD thesis Risk, Ambiguity, and Decision.

Topics: decision theory, game theory

1,650
1.7K

Jul 6, 2008
07/08

by
Jordan, Camille, 1838-1922

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Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.

Topics: Group theory, Galois theory

Source: http://books.google.com/books?id=TzQAAAAAQAAJ&oe=UTF-8

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129

Jul 31, 2019
07/19

by
Weyl, Hermann, 1885-1955

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xxii, 422 p

Topics: Group theory, Quantum theory

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Nov 22, 2021
11/21

by
Hamming, R. W. (Richard Wesley), 1915-1998

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xii, 239 p. : 24 cm

Topics: Coding theory, Information theory