Record Nr.

UNINA9910459795903321

Autore

Brubaker Ben <1976->

Titolo

Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg

Pubbl/distr/stampa


Princeton, N.J., : Princeton University Press, c2011

ISBN

1-283-01338-X

9786613013385

1-4008-3899-1

Edizione

[Course Book]

Descrizione fisica

1 online resource (173 p.)

Collana

Annals of mathematics studies ; ; no. 175

Altri autori (Persone)

BumpDaniel <1952->

FriedbergSolomon <1958->

Disciplina

515/.243

Soggetti

Dirichlet series

Weyl groups

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Front matter -- Contents -- Preface -- Chapter One. Type A Weyl Group Multiple Dirichlet Series -- Chapter Two. Crystals and Gelfand-Tsetlin Patterns -- Chapter Three. Duality -- Chapter Four. Whittaker Functions -- Chapter Five. Tokuyama's Theorem -- Chapter Six. Outline of the Proof -- Chapter Seven. Statement B Implies Statement A -- Chapter Eight. Cartoons -- Chapter Nine. Snakes -- Chapter Ten. Noncritical Resonances -- Chapter Eleven. Types -- Chapter Twelve. Knowability -- Chapter Thirteen. The Reduction to Statement D -- Chapter Fourteen. Statement E Implies Statement D -- Chapter Fifteen. Evaluation of ΛΓ and ΛΔ, and Statement G -- Chapter Sixteen. Concurrence -- Chapter Seventeen. Conclusion of the Proof -- Chapter Eighteen. Statement B and Crystal Graphs -- Chapter Nineteen. Statement B and the Yang-Baxter Equation -- Chapter Twenty. Crystals and p-adic Integration -- Bibliography -- Notation -- Index

Sommario/riassunto

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple

Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.

Record Nr.

UNINA9910818967503321

Autore

Bass Richard F.

Titolo

Cutting Brownian paths / / Richard F. Bass, Krzysztof Burdzy

Pubbl/distr/stampa


Providence, Rhode Island : , : American Mathematical Society, , [1999]
©1999

ISBN

1-4704-0246-7

Descrizione fisica

1 online resource (113 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 657

Disciplina

510 s

530.4/75