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# Geometric Methods in Representation Theory Seminar – Mikhail Kapranov (Kavli IPMU at Tokyo)

## October 25 @ 3:30 pm - 4:30 pm

**Operadic analysis of parabolic induction**

**Abstract:** The construction of various types of Hall algebas can be seen as an instance of the parabolic induction formalism. More precisely, this formalism is used to arrange various linear data associated to groups GL_n for all n (e.g., cohomology of the moduli spaces of vector bundles) into an associative algebra. But parabolic induction makes sense for arbitrary reductive groups. The talk, based on joint work in progress with V. Schechtman, O. Schiffman and J. Yuan, proposes an operad-style approach to formalize the algebra-like structures provided by all reductive groups taken together. The corresponding “double” structures (reducing to graded bi/Hopf algebras for the GL_n series) are important for the problem of classifying perverse sheaves on the adjoint quotients h/W.