**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)

### Algebra Seminar

# Involutions on the affine Grassmannian and moduli spaces of principal bundles

### Anthony Henderson (Sydney)

##
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.