WHITTAKER FUNCTIONS AND DEMAZURE CHARACTERS
نویسندگان
چکیده
منابع مشابه
Whittaker Functions and Demazure Characters
In this paper, we consider how to express an Iwahori–Whittaker function through Demazure characters. Under some interesting combinatorial conditions, we obtain an explicit formula and thereby a generalization of the Casselman–Shalika formula. Under the same conditions, we compute the transition matrix between two natural bases for the space of Iwahori fixed vectors of an induced representation ...
متن کاملNonsymmetric Macdonald Polynomials and Demazure Characters
We establish a connection between a specialization of the nonsymmetric Macdonald polynomials and the Demazure characters of the corresponding affine Kac-Moody algebra. This allows us to obtain a representation-theoretical interpretation of the coefficients of the expansion of the specialized symmetric Macdonald polynomials in the basis formed by the irreducible characters of the associated fini...
متن کاملAnna Pun Drexel University “ On Decomposition of the Product of Demazure Atom and Demazure Characters ”
It is an open problem to prove the Schubert positivity property combinatorially. Recently Haglund, Mason, Remmel, van Willigenburg et al. have studied the skyline fillings (a tableau-combinatorial object giving a combinatorial description to nonsymmetric MacDonald polynomials , proved by Haglund, Haiman and Loehr) specifically for the case of Demazure atoms (atoms) and key polynomials (keys). T...
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The Schur function indexed by a partition λ with at most n parts is the sum of the weight monomials for the Young tableaux of shape λ. Let π be an npermutation. We give two descriptions of the tableaux that contribute their monomials to the key polynomial indexed by π and λ. (These polynomials are the characters of the Demazure modules for GL(n).) The “atom” indexed by π is the sum of weight mo...
متن کاملOn the Connection Between Macdonald Polynomials and Demazure Characters
We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for ŝl(n). This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials.
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ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2017
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748017000214