Speaker
Description
Graded braided Hopf algebras (such as the Hall algebra of a curve over $F_q$) correspond to factorizing systems of perverse sheaves on the symmetric products of the complex line. The talk will present an analog of this correspondence for an arbitrary complex reductive group G where the role of the symmetric product is played by the quotient h/W. We exhibit an algebra C so that C-Mod = Perv(h/W) with respect to the natural stratification. The relations in C include the Langlands formula for the constant term of Eisenstein series in the theory of automorphic forms. This formula generalizes the compatibilty between multiplication and comultiplication in a graded braided Hopf algebra (obtained for G=$GL_n$.
The algebra C is the W-invariant subalgebra in the algebra B describing perverse sheaves on h. This matches nicely the description of h/W as the spectrum of the algebra of invariants. Joint work with V. Schechtman, O. Schiffmann and J. Yuan.
