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Quadratic transformations of Macdonald and Koornwinder polynomials

Rains, Eric M. and Vazirani, Monica J. (2006) Quadratic transformations of Macdonald and Koornwinder polynomials. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20171010-113111196

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Abstract

When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form. A number of q-analogues of this fact were conjectured in [8]; the present paper proves most of those conjectures, as well as some new identities suggested by the proof technique. The proof involves showing that a nonsymmetric version of the relevant integral is annihilated by a suitable ideal of the affine Hecke algebra, and that any such annihilated functional satisfies the desired vanishing property. This does not, however, give rise to vanishing identities for the standard nonsymmetric Macdonald and Koornwinder polynomials; we discuss the required modification to these polynomials to support such results.


Item Type:Report or Paper (Discussion Paper)
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https://arxiv.org/abs/math/0606204arXivDiscussion Paper
Record Number:CaltechAUTHORS:20171010-113111196
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171010-113111196
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82255
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:10 Oct 2017 20:52
Last Modified:04 Apr 2019 23:14

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