A quiver for the BGG category O: recent developments and a combinatorial challengeMaxim VybornovMIT
February 11,

ABSTRACT


Explicit description of representationtheoretic categories in terms of quivers had been a significant part of I.M. Gelfand's philosophy in the 60s and 70s. The problem of finding such a description for the BGG category 0, though partially solved by the historic breakthrough of the KazhdanLusztig theory, defied the complete solution for about 30 years now. In this talk we use our results on perverse sheaves to explain how this problem is now reduced to a combinatorial challenge of finding intertwiners between certain representations of the polynomial coinvariants of the Weyl group. Our construction of perverse sheaves, or ICmodules, does not use the derived categories and tstructures and makes sense for a wide variety of stratified spaces including toric varieties, affine Grassmannians, and locally symmetric spaces. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

