1111.0515 (Oleg Chalykh et al.)

Orthogonality relations and Cherednik identities for multivariable
Baker-Akhiezer functions    [PDF]

Oleg Chalykh, Pavel Etingof

We establish orthogonality relations for the Baker-Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik-Macdonald-Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik-Macdonald-Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new quantum integrable models of Macdonald-Ruijsenaars type.

View original: http://arxiv.org/abs/1111.0515