Chennai Mathematical Institute


3.30 p.m., Seminar Hall
Kempf-Laksov-Damon determinant formula in K-theory

Takeshi Ikeda
Okayama University of Science, Japan.


We consider a degeneracy locus in the Grassmannian bundle of a vector bundle E defined by a Schubert type condition. In 1970’s, a remarkable determinant formula for the degeneracy loci class in Chow ring of the Grassmannian bundle was proved by Kempf and Laksov, and independently by Damon. This determinant formula extends the previous special case proved by Porteous. The KLD-formula was rediscovered by Lakshimibai, Raghavan, and Sankaran in the context of torus equivariant cohomology in 2005. The polynomial appearing in these works had been also known as the factorial Schur function introduced by Biedenharn and Louck in 1989. The aim of this talk is to explain a similar determinant formula of the class of the structure sheaf of the degeneracy loci in the K-ring of coherent sheaves on the Grassmannian bundle. This leads to a new determinant formula for the factorial Grothendieck polynomial studied by McNamara. If time permits, I also discuss the analogous Pfaffian formula for isotropic vector bundles.