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• W2176533062 abstract "This thesis deals with Harish-Chandra bimodules of rational Cherednik algebras Hk at regular parameter values k, that is those k for which Hk is a simple algebra. Rational Cherednik algebras can be associated to any reflection representation of a complex reflection group Γ. The second chapter presents a review of some important results regarding rational Cherednik algebras and their category Ok, which will be frequently used throughout. The third chapter contains basic results about Harish-Chandra bimodules and the structure of the category HCk of Harish-Chandra bimodules, many of which are new in the context of complex reflection groups but have known analogues for real reflection groups at integral parameter values by work of Berest-Etingof-Ginzburg in [BEG03b]. In particular we show that if k is regular, then HCk is a semisimple tensor category and is equivalent to a tensor-closed subcategory of modules of the associated Hecke algebra. Using work of I. Losev in [Los11a], we also deduce that HCk is equivalent as a tensor category to repC (Γ/Nk), the representation category of a quotient of the complex reflection group Γ. This extends previous results for the case of integral k. We manage to obtain some numerical consequences for the presentation of the Hecke algebra of Γ, which is linked to Hk and Ok via the KZk-functor. The fourth chapter again is a review of standard results on Morita equivalences between rings and integral shift functors giving Morita equivalences between rational Cherednik algebras and their tensor categories of Harish-Chandra bimodules at different regular parameter values. The case of integral parameter values k is discussed briefly, going back to Berest-Etingof-Ginzburg in [BEG03b] and Berest-Chalykh in [BC09]. The fifth chapter gives a complete description of Nk and its dependence on k (still for k regular) for the case that Γ is cyclic. In chapter 6 we deal with finite-dimensional Harish-Chandra bimodules of rational Cherednik algebras associated to cyclic groups, compute the quiver of that category and derive a criterion for wildness of HCk in the cyclic case. Chapter 7 finally extends a classification of the structure of HCk as a tensor category for regular k to finite irreducible Coxeter groups." @default.
• W2176533062 created "2016-06-24" @default.
• W2176533062 creator A5011898753 @default.
• W2176533062 date "2012-09-01" @default.
• W2176533062 modified "2023-10-17" @default.
• W2176533062 title "On Harish-Chandra bimodules of rational Cherednik algebras at regular parameter values" @default.
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