SMS scnews item created by Oded Yacobi at Wed 18 Nov 2015 1227
Type: Seminar
Distribution: World
Expiry: 25 Nov 2015
Calendar1: 20 Nov 2015 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Involutions on the affine Grassmannian and moduli spaces of principal bundles
Auth: oyacobi@p637.pc (assumed)

Involutions on the affine Grassmannian and moduli spaces of principal bundles

Friday 20 Nov, 12-1pm, Place: Carslaw 375

Let $$G$$ be a connected reductive group over $$\mathbb{C}$$. For reasons related to our work on nilpotent orbits, Pramod Achar and I were led to study a certain involution of an open subset of the affine Grassmannian of $$G$$. In this talk I will explain a new interpretation of this involution: it corresponds to the action of the nontrivial Weyl group element of $$\mathrm{SL}(2)$$ on the framed moduli space of $$\mathbb{G}_m$$-equivariant principal $$G$$-bundles on $$\mathbb{P}^2$$. As a result, the fixed-point set of the involution can be partitioned into strata indexed by conjugacy classes of homomorphisms $$N\to G$$ where $$N$$ is the normalizer of $$\mathbb{G}_m$$ in $$\mathrm{SL}(2)$$. In the case where $$G=\mathrm{GL}(r)$$, these strata are isomorphic to quiver varieties of type D.

Actions: