Vai al contenuto principale della pagina

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



(Visualizza in formato marc)    (Visualizza in BIBFRAME)

Autore: Brubaker Ben <1976-> Visualizza persona
Titolo: Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg Visualizza cluster
Pubblicazione: Princeton, N.J., : Princeton University Press, c2011
Edizione: Course Book
Descrizione fisica: 1 online resource (173 p.)
Disciplina: 515/.243
Soggetto topico: Dirichlet series
Weyl groups
Soggetto genere / forma: Electronic books.
Soggetto non controllato: BZL pattern
Class I.
Eisenstein series
Euler product
Gauss sum
Gelfand-Tsetlin pattern
Kashiwara operator
Kashiwara's crystal
Knowability Lemma
Kostant partition function
Riemann zeta function
Schur polynomial
Schützenberger involution
Snake Lemma
Statement A.
Statement B.
Statement C.
Statement D.
Statement E.
Statement F.
Statement G.
Tokuyama's Theorem
Weyl character formula
Weyl denominator
Weyl group multiple Dirichlet series
Weyl vector
Whittaker coefficient
Whittaker function
Yang-Baxter equation
Yang–Baxter equation
accordion
adele group
affine linear transformation
analytic continuation
analytic number theory
archimedean place
basis vector
bijection
bookkeeping
box-circle duality
boxing
canonical indexings
cardinality
cartoon
circling
class
combinatorial identity
concurrence
critical resonance
crystal base
crystal graph
crystal
divisibility condition
double sum
episode
equivalence relation
f-packet
free abelian group
functional equation
generating function
global field
ice-type model
inclusion-exclusion
indexing
involution
isomorphism
knowability
maximality
nodal signature
nonarchimedean local field
noncritical resonance
nonzero contribution
p-adic group
p-adic integral
p-adic integration
partition function
polynomial
preaccordion
prototype
reduced root system
representation theory
residue class field
resonance
resotope
row sums
row transfer matrix
short pattern
six-vertex model
snakes
statistical mechanics
subsignature
tableaux
type
Γ-equivalence class
Γ-swap
Altri autori: BumpDaniel <1952->  
FriedbergSolomon <1958->  
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.
Titolo autorizzato: Weyl group multiple Dirichlet  Visualizza cluster
ISBN: 1-283-01338-X
9786613013385
1-4008-3899-1
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910459795903321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of mathematics studies ; ; no. 175.