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THE STEINBERG TORUS OF A WEYL GROUP AS A MODULE OVER THE COXETER COMPLEX
Hyperplane arrangement Coxeter complex Steinberg torus
2015/8/14
Associated to each irreducible crystallographic root system , there is a certain
cell complex structure on the torus obtained as the quotient of the ambient space by the
coroot lattice of . This i...
Twisted Weyl Group Multiple Dirichlet Series: The Stable Case
Stable Case Multiple Dirichlet Series
2015/7/6
Weyl group multiple Dirichlet series were associated with a root system Φ and a number
field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] an...
Given a root system Φ of rank r and a global field F containing the n-th
roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose
coefficients are n-th ...
Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory
Type A Combinatorial Theory Dirichlet Series
2015/7/6
Speci cally, two distinct versions of the Gelfand-Tsetlin de nition were given. It
is not apparent that they are equal. Either of these de nitions is purely local in that
it speci es the p-part of t...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
Coefficients of the n-fold Theta Function and Weyl Group Multiple Dirichlet Series
Dirichlet Series Theta Function
2015/7/6
We establish a link between certain Whittaker coecients of the generalized
metaplectic theta functions, rst studied by Kazhdan and Patterson [14], and
the coecients of the stable Weyl group multi...
Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
Rational Function Field Multiple Dirichlet
2014/12/8
Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreduc...
For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants...
Lower boundary hyperplanes of the canonical left cells in the affine Weyl group Wa（An-1）
affine Weyl groups left cells hyperplanes
2011/9/28
Let F be any canonical left cell of the affine Weyl group Wa of type A. We describe the lower boundary hyperplanes for F, which answer two questions of Humphreys.
Snub 24-Cell Derived from the Coxeter-Weyl Group W(D4)
Snub 24-Cell the Coxeter-Weyl Group W(D4)
2011/7/26
Snub 24-Cell Derived from the Coxeter-Weyl Group W(D4).
On certain varieties attached to a Weyl group element
certain varieties Weyl group element
2011/1/20
0. Introduction and statement of results 0.1. Let k be an algebraically closed field. Let G be a connected reductive algebraic group over k. We assume that we are in one of the following two cases.(1)...