Ben Brubaker
Whittaker Functions and Demazure Operators.
Пнд, 11/21/2011 - 15:01 — SomNambulAuthors: Ben Brubaker, Daniel Bump, Anthony Licata
Subjects: Representation Theory
AbstractWe consider a natural basis of the Iwahori fixed vectors in the Whittaker
model of an unramified principal series representation of a split semisimple p-
adic group, indexed by the Weyl group. We show that the elements of this basis
may be computed from one another by applying Demazure-Lusztig operators. The
precise identities involve correction terms, which may be calculated by a
combinatorial algorithm that is identical to the computation of the fibers of
the Bott-Samelson resolution of a Schubert variety.- Читать далее
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Weyl group multiple Dirichlet series of type C.
Пнд, 03/08/2010 - 16:01 — SomNambulAuthors: Ben Brubaker, Jennifer Beineke, Sharon Frechette
Subjects: Number Theory
AbstractWe develop the theory of Weyl group multiple Dirichlet series for root
systems of type C. For an arbitrary root system of rank r and a positive
integer n, these are Dirichlet series in r complex variables with analytic
continuation and functional equations isomorphic to the associated Weyl group.
In type C, they conjecturally arise from the Fourier-Whittaker coefficients of
minimal parabolic Eisenstein series on an n-fold metaplectic cover of SO(2r+1).
For any odd n, we construct an infinite family of Dirichlet series
conjecturally satisfying the above analytic properties.- Читать далее
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Schur Polynomials and the Yang-Baxter equation.
Пнд, 12/07/2009 - 16:01 — SomNambulAuthors: Ben Brubaker, Daniel Bump, Solomon Friedberg
Subjects: Combinatorics
AbstractWe show that within the six-vertex model there is a parametrized Yang-Baxter
equation with nonabelian parameter group GL(2)xGL(1) at the center of the
disordered regime. As an application we rederive deformations of the Weyl
character formule of Tokuyama and of Hamel and King.
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