Felix Klein Seminar
Speaker: Ben Wyser
University of Illinois, Urbana-Champaign
It is well-known that the Schubert cycles, or fundamental classes of Schubert varieties, form an integer basis for the cohomology ring of the flag manifold. The structure constants with respect to this integer basis are known to be non-negative, and are readily computable. Yet it remains an open problem, even in type A, to give a positive formula for a general structure constant. Wyser will explain how certain of these structure constants can be computed positively by applying a theorem of M. Brion to Richardson varieties (intersections of Schubert varieties with opposite Schubert varieties) stable under spherical Levi subgroups. Wyser will discuss some of the combinatorial details in the case which is likely of most interest, namely type A richardson varieties stable under the Levi subgroups GL(p,\C)\timesGL(q,\C)\subsetGL(p+q,\C).
Originally published at math.nd.edu.