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Affine Hecke Algebras via DAHA. (arXiv:1707.03519v2 [math.QA] UPDATED)

来源于:arXiv
This note is mostly based on the lecture delivered at the conference "Algebraic Analysis and Representation Theory" in honor of Professor Masaki Kashiwara's 70th birthday. Its main topic is the project aimed at obtaining the Plancherel formula for the regular representation of Affine Hecke Algebras (AHA) as the limit $q\to 0$ of the integral-type formulas for DAHA inner products in the polynomial and related modules. The integrals for the latter as $\Re k>0$ (in the DAHA parameters) must be analytically continued to negative $\Re k$, which is a $q$-generalization of "picking up residues" due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. We arrive at finite sums of integrals over double affine residual subtori. This is not related to the DAHA reducibility of the polynomial and similar modules; the procedure is nontrivial for any $\Re k<0$. Though such formulas can be used for the DAHA stratification when these modules become reducible for singular 查看全文>>