Polynomials for Symmetric Orbit Closures on the Flag Variety
by Dr Benjamin Wyser
Abstract: The variety of complete flags has many interesting subvarieties. The most famous are the Schubert varieties. In 1982, Lascoux and Schutzenberger defined Schubert polynomials as natural representatives of their cohomology classes. These polynomials have been studied extensively using a wide range of tools from combinatorics, representation theory and algebraic geometry.
In the representation theory of real Lie groups, one finds analogues of the Schubert varieties. These are the closures of orbits on the flag variety under the action of a certain symmetric subgroup. I will discuss joint work with Alexander Yong in which we compute analogues of Schubert polynomials in this setting. I will describe the computation and also discuss some combinatorial and geometric properties of our polynomials.