A formula for the cohomology and K-class of a regular Hessenberg variety.

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. [ABSTRACT FROM AUTHOR]