Polynomials for GL_p x GL_q orbit closures in the flag variety
Representation Theory
2014-11-06 v2 Algebraic Geometry
Combinatorics
Abstract
The subgroup K=GL_p x GL_q of GL_{p+q} acts on the (complex) flag variety GL_{p+q}/B with finitely many orbits. We introduce a family of polynomials that specializes to representatives for cohomology classes of the orbit closures in the Borel model. We define and study K-orbit determinantal ideals to support the geometric naturality of these representatives. Using a modification of these ideals, we describe an analogy between two local singularity measures: the H-polynomials and the Kazhdan-Lusztig-Vogan polynomials.
Keywords
Cite
@article{arxiv.1308.2632,
title = {Polynomials for GL_p x GL_q orbit closures in the flag variety},
author = {Benjamin J. Wyser and Alexander Yong},
journal= {arXiv preprint arXiv:1308.2632},
year = {2014}
}
Comments
25 pages; v2 to appear in Selecta Math