Quadratic transformations of Macdonald and Koornwinder polynomials
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 qanalogues of this fact were conjectured in math.QA/0112035; 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606204
 Bibcode:
 2006math......6204R
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Combinatorics
 EPrint:
 32 pages LaTeX, 10 xfig figures