Nonsymmetric Macdonald polynomials and matrix coefficients for unramified principal series

Details Nonsymmetric Macdonald polynomials and matrix coefficients for unramified principal series Nonsymmetric Macdonald polynomials and matrix coefficients for unramified principal series

2004-07-03

arxiv.org/abs/math/0407044v5

Mathematics

Quantum Algebra

25pg

Scientific paper

We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p--adic fields as matrix coefficients for the unramified principal series representations. The result is the nonsymmetric counterpart of a classical result relating the same limit of the symmetric Macdonald polynomials to zonal spherical functions on groups of p--adic type.

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