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There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras which are quantizations of symplectic singularities (Losev). What is the meaning of Harish-Chandra bimodules in terms of representation theory of the underlying algebra/its category O? Are Harish-Chandra bimodules related to the classical notion of Harish-Chandra modules?

There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras which are quantizations of symplectic singularities (Losev). What is the meaning of Harish-Chandra bimodules in terms of representation theory of the underlying algebra/its category O? Are Harish-Chandra bimodules related to the classical notion of Harish-Chandra modules?

There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras which are quantizations of symplectic singularities (Losev). What is the meaning of Harish-Chandra bimodules in terms of representation theory of the underlying algebra/its category O? Are Harish-Chandra bimodules related to the classical notion of Harish-Chandra modules?

There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras which are quantizations of symplectic singularities (Losev). What is the meaning of Harish-Chandra bimodules in terms of representation theory of the underlying algebra/its category O? Are Harish-Chandra bimodules related to the classical notion of Harish-Chandra modules?

There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras associated to resolutions of symplectic singularities. What is the meaning of Harish-Chandra bimodules in terms of representation theory of the underlying algebra/its category O? Are Harish-Chandra bimodules related to the classical notion of Harish-Chandra modules?

There are many recent papers on classification of Harish-Chandra bimodules for rational Cherednik algebras and, more generally, non-commutative algebras which are quantizations of symplectic singularities (Losev). What is the meaning of Harish-Chandra bimodules in terms of representation theory of the underlying algebra/its category O? Are Harish-Chandra bimodules related to the classical notion of Harish-Chandra modules?