Published on *www.math.tifr.res.in* (http://www.math.tifr.res.in)

Massachusetts Institute of Technology, USA

December 26, 2013

: This talk is based in part on a joint work with D. Vogan. The set of involutions in a Weyl group (for example the symmetric group) can be viewed as a basis of a vector space on which the Weyl group acts. This representation of the Weyl group can be deformed to a q-analogue which is a representation of the Hecke algebra. From this representation one can extract some new polynomials indexed by a pair of involutions which generalize the polynomials introduced in 1979 in my paper with Kazhdan.