Special Year Seminar I

We will discuss combinatorial and algebraic aspects of regular Hessenberg varieties, a large class of subvarieties of the flag variety G/B. For the special case of Peterson varieties, we show their equivariant structure constants are non-negative, and present an equivariant Chevalley Monk formula in all Lie types. We also present a positive formula for all equivariant structure constants of the Peterson variety in type A. Time permitting, we will discuss a conjecture on the equivariant K-theory of Peterson varieties.

This talk is based on separate collaborations with Brent Gorbutt, Rahul Singh and Leo Mihalcea.