Abstract
We investigate the t=qk specialization of the homogeneous symmetric Macdonald polynomials Pλ(X;q,t). We show an identity relating the polynomials Pλ(X;q,qk) and Pλ(1−q1−qkX;q,qk). As a consequence, we describe an operator whose eigenvalues characterize the polynomials Pλ(X;q,qk).
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