Degeneracy Loci Classes in $K$-theory - Determinantal and Pfaffian Formula -
Abstract
We prove a determinantal formula and Pfaffian formulas that respectively describe the -theoretic degeneracy loci classes for Grassmann bundles and for symplectic Grassmann and odd orthogonal bundles. The former generalizes Damon--Kempf--Laksov's determinantal formula and the latter generalize Pragacz--Kazarian's formula for the Chow ring. As an application, we introduce the factorial -functions representing the torus equivariant -theoretic Schubert classes of the symplectic and the odd orthogonal Grassmannians, which generalize the (double) theta polynomials of Buch--Kresch--Tamvakis and Tamvakis--Wilson.
Keywords
Cite
@article{arxiv.1504.02828,
title = {Degeneracy Loci Classes in $K$-theory - Determinantal and Pfaffian Formula -},
author = {Thomas Hudson and Takeshi Ikeda and Tomoo Matsumura and Hiroshi Naruse},
journal= {arXiv preprint arXiv:1504.02828},
year = {2018}
}
Comments
This is a major update. In particular, we extended the results in arXiv:1602.04448 and included in this version. We modified the expositions in several places from the previous version