Year: 2026
Type: preprint
Abstract: Skew-symmetric matrix Schubert varieties are determinantal varieties obtained by intersecting matrix Schubert varieties with the space of skew-symmetric matrices. They are closely related to the orbit closures of the symplectic group action on the flag variety, and their torus-equivariant K-classes are the symplectic Grothendieck polynomials. We compute the Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties by giving a combinatorial formula for the degree of symplectic Grothendieck polynomials. In addition, we characterize the highest-degree homogeneous component of a symplectic Grothendieck polynomial and compute the maximal Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties.
Source: arXiv (Cornell University)
Author: Chou, Jack Chen-An
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214014735