3
$\begingroup$

I am interested in finding a set of functions $f(z_1,\cdots ,z_k;q,\,t)$, conjecturally polynomials, which depend on two parameters $(q,t)$ and an integer $k$, and are orthogonal under the following measure

$\prod_{i=1}^k \frac{(z_i^{\pm2};q)}{(t \, z_i^{\pm1}\,z_{i+1}^{\pm1};q)}$

Here, the indices are defined mod $k$, i.e. $i+1 = (i+1)\, mod\, k$. For $k=1$ the set of functions is that of $A_1$ Macdonald polynomials. Are such functions discussed somewhere in the literature? (These functions should be also eigenfunctions of certain difference operators which can be explicitly written down.)

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.