Nonsymmetric Macdonald polynomials and Demazure characters

By B. Ion. 2001

144 citations recorded by the source corpus.

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 finite Lie algebra.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1355876a81aee3b3a62629e9f965aee12b73c84f

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Weyl modules and $$q$$q-Whittaker functions (2012, background): “2 It is important to emphasize that the definition of Demazure modules used in this paper (as fibers of Weyl modules) is not obviously equivalent to the standard definition used in [18]; however, the equivalence of the two definitions is proved in [4] in type A, and in [12] in general.”
An explicit construction of type A Demazure atoms (2007, background): “A similar connection exists between nonsymmetric Macdonald polynomials specialized to q = t = ∞ and Demazure characters of the corresponding affine KacMoody algebra [4].”
Whittaker functions and Demazure operators (2011, methodology): “Ion has shown that Eλ(q,∞) are Demazure characters of basic representations of affine Kac-Moody groups [17] and Eλ(∞, t) are matrix coefficients for M(τ) using the spherical functional [18].”