Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction

The problem of classification of perverse sheaves on the quotient h/W for a semisimple Lie algebra g has an explicit answer which turns out to be related to the algebraic properties of induction and restriction operations for parabolic subalgebras in g. For g=gl(n) we get a relation between factorizing systems of perverse sheaves on the symmetric products of the complex line and braided Hopf algebras. Joint work with V. Schechtman.



Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo