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Weyl Group Multiple Dirichlet SeriesType A Combinatorial Theory (AM-175)$
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Ben Brubaker, Daniel Bump, and Solomon Friedberg

Print publication date: 2011

Print ISBN-13: 9780691150659

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691150659.001.0001

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Tokuyama’s Theorem

Tokuyama’s Theorem

Chapter:
(p.31) Chapter Five Tokuyama’s Theorem
Source:
Weyl Group Multiple Dirichlet Series
Author(s):

Ben Brubaker

Daniel Bump

Solomon Friedberg

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691150659.003.0005

This chapter introduces the Tokuyama's Theorem, first by writing the Weyl character formula and restating Schur polynomials, the values of the Whittaker function multiplied by the normalization constant. The λ‎-parts of Whittaker coefficients of Eisenstein series can be profitably regarded as a deformation of the numerator in the Weyl character formula. This leads to deformations of the Weyl character formula. Tokuyama gave such a deformation. It is an expression of ssubscript Greek small letter lamda(z) as a ratio of a numerator to a denominator. The denominator is a deformation of the Weyl denominator, and the numerator is a sum over Gelfand-Tsetlin patterns with top row λ‎ + ρ‎.

Keywords:   Tokuyama's Theorem, Weyl character formula, Schur polynomial, Whittaker function, Whittaker coefficient, Eisenstein series, Weyl denominator, Gelfand-Tsetlin pattern

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