Journal of Pure and Applied Algebra
Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator X and a nondecreasing function h. The family of Hessenberg varieties for regular X is particularly important: they are used in quantum cohomology, in combinatorial and geometric representation theory, in Schubert calculus and affine Schubert calculus. We show that the classes of a regular Hessenberg variety in the cohomology and K-theory of the flag variety are given by making certain substitutions in the Schubert polynomial (respectively Grothendieck polynomial) for a permutation that depends only on h. Our formula and our methods are different from a recent result of Abe, Fujita, and Zeng that gives the class of a regular Hessenberg variety with more restrictions on h than here.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.
Insko, Erik; Tymoczko, Julianna; and Woo, Alexander, "A Formula for the Cohomology and K-Class of a Regular Hessenberg Variety" (2020). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.