Quadratic transformations of Macdonald and Koornwinder polynomials
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 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.