A quiver for the BGG category O: recent developments and a combinatorial challenge

Maxim Vybornov

MIT

February 11,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

Explicit description of representation-theoretic 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 Kazhdan-Lusztig 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 IC-modules, does not use the derived categories and t-structures and makes sense for a wide variety of stratified spaces including toric varieties, affine Grassmannians, and locally symmetric spaces.


Speaker's Contact Info: vybornov(at-sign)math.mit.edu


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