The Character Theory of a Complex Group

Understand

We apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups.

• Our focus is the Hecke category of Borel-equivariant D-modules on the flag variety of a complex reductive group G (equivalently, the category of Harish Chandra bimodules of trivial central character) and its monodromic variant.
• The Hecke category is a categorified analogue of the finite Hecke algebra, which is a finite-dimensional semi-simple symmetric Frobenius algebra.
• We establish parallel properties of the Hecke category, showing it is a two-dualizable Calabi-Yau monoidal category, so that in particular, its monoidal (Drinfeld) center and trace coincide.