多元Baker-Akhiezer函数的正交关系和Cherednik恒等式
Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions
摘要：
建立了Macdonald差分算子的Baker-Akhiezer（BA）本征函数的正交关系.我们还得到了一个版本的Cherednik-Macdonald-Mehta积分这些功能。作为推论，我们给出了Macdonald多项式的范数恒等式和Cherednik-Macdonald-Mehta积分的一个简单推导。在第一作者所写的附录中，我们证明了BA函数的一个求和公式。我们还考虑了更一般的身份的Cherednik型，我们用它来介绍和构造更一般的，扭曲BA功能。这导致了新的量子可积模型的Macdonald-Ruijsenaars类型的建设。
英文摘要：
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.
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