James Parkinson

Friday 31st August, 12.05-12.55pm, Carslaw 373

Path combinatorics in loop groups

In this talk we discuss some joint work with Arun Ram on the combinatorics of the loop group G=G(k((t))), where G(.) is a Kac-Moody-Tits group functor. The points of the affine flag variety G/I (with I an Iwahori subgroup) can be indexed by generalised labeled Littelmann paths, which control various double coset decompositions of G.

In the case when G(.) is of finite type this model can be made very explicit, since the loop group G=G(k((t))) is (essentially) the affine Kac-Moody group. In this case the combinatorics of labeled Littelmann paths is very closely related to retractions in the affine building.