Event
William Slofstra, University of Waterloo
Smooth Schubert varieties of affine type.
A natural question about Schubert varieties is: when is a Schubert variety smooth? In finite type, this question is completely solved. Not only can we recognize smooth Schubert varieties using pattern avoidance, but we can explicitly construct all smooth Schubert varieties as iterated fibre bundles starting from a short list of known manifolds. Much less is known about smooth Schubert varieties of affine type. In this talk, I will discuss joint work with Ed Richmond in which we show that everything we know about finite type can be extended to affine type A. In particular, we show that every smooth Schubert variety of affine type A is an iterated fibre bundle of Grassmannians. I will also highlight some examples showing that interesting things can happen in affine type, including joint work with Lakshmibai and Ravikumar showing that the cotangent bundle to a cominuscule Grassmannian can be embedded in a smooth Schubert variety of an affine two-step partial flag variety.