Work

K-Orbit closures and Hessenberg varieties

Year: 2025

Type: article

Abstract: This article explores the relationship between Hessenberg varieties associated with semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the general linear group. We establish the specific conditions under which these semisimple Hessenberg varieties are irreducible. We determine the dimension of each irreducible Hessenberg variety under consideration and show that the number of such varieties is a Catalan number. We then apply a theorem of Brion to compute a polynomial representative for the cohomology class of each such variety. Additionally, we calculate the intersections of a standard (Schubert) hyperplane section of the flag variety with each of our Hessenberg varieties and prove that this intersection possesses a cohomological multiplicity-free property.

Source: Forum of Mathematics Sigma

DOI: 10.1017/fms.2025.10063

Authors: Mahir Bilen Can, Martha Precup, John Shareshian, Özlem Uğurlu

Institutions: Tulane University, Washington University in St. Louis, Saint Louis University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,650

Funders: National Science Foundation, Louisiana Board of Regents