Representation theory seminars: Mackey formula for representations of reductive groups

Speaker: Lucien Hennecart (CNRS)

Abstract: In this talk, I will describe the construction of induction and restriction morphisms on the critical cohomology associated with a function on a representation of a reductive group. The induction morphisms play a key role in obtaining a cohomological integrality decomposition, which is a decomposition into finite-dimensional pieces with enumerative significance. The building blocks of this decomposition are given by the BPS cohomology. After discussing this decomposition and its geometric meaning, I will present a cohomological version of the Mackey formula that relates the induction and restriction operations. I will also present examples of the formalism in low dimensions. This can be seen as a generalization to more general stacks of the cohomological Hall algebra multiplication and its localized restriction.

Time: 2025-06-23 16:00:00

Location: R1210, SIMIS