Combinatorial identities arising from the representation theory and geometry of rational Cherednik algebras

Tomasz Przezdziecki

Friday 10th June, 2016 16:00-17:00 Maths 326


We will discuss rational Cherednik algebras associated to generalized symmetric groups at parameter t=0. These algebras have a large centre, and its spectrum is an affine variety isomorphic to the Calogero-Moser space. The latter can also be constructed as a Nakajima quiver variety. These varieties are endowed with a torus action with finitely many fixed points. Studying the characters of the fibres of tautological vector bundles at these fixed points allows us to recover and generalize a q-analog of the hook-length formula.

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