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Lie Groups Quantum Mathematics Seminar

Dirac operators for rational Cherednik algebras and Calogero-Moser families

Dan Ciubotaru, University of Oxford

Location:  Hill 705
Date & time: Friday, 14 September 2018 at 12:00PM - 1:00PM

  • Abstract:   I will first define and present the main properties of the Dirac operator for rational Cherednik algebra. Then I will explain the connection between Vogan's Dirac morphism in this setting and Gordon's partition of irreducible representations of a complex reflection group into families defined using the geometry of the generalized Calogero-Moser space. A conjecture of Gordon, Martino, and Rouquier (verified in many cases by Martino, Bellamy, Thiel) relates the Calogero-Moser families to Lusztig's families (Kazhdan-Lusztig double cells). Finally, I will explain how Dirac cohomogy can help towards verifying this conjectural relation.