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.
After the seminar we will take the speaker to lunch.
See the Algebra Seminar web page for information about other seminars in the series.
Anthony Henderson email@example.com.