Math Seminars.
Anders Buch (U of C),
Formulas for Degeneracy Loci.
I will describe a new class of polynomials which describe the
cohomology class of a very general type of degeneracy loci,
associated to a sequence of vector bundle maps and arbitrary
rank conditions on these maps and their compositions. These
polynomials generalize and give new formulas for all known types
of Schubert polynomials. Our polynomials are expressed as a
linear combination of products of Schur polynomials. We
conjecture that all coefficients are non-negative, and given by
a generalized Littlewood-Richardson rule. This is joint work
with William Fulton.