# On the K-theoretic fundamental classes of Deligne-Lusztig varieties

## TL;DR

This paper expresses the K-theoretic classes of Deligne-Lusztig varieties as explicit polynomials, linking geometric degeneracy loci with algebraic formulas in the context of flag varieties.

## Contribution

It provides an explicit formula for the K-theoretic classes of Deligne-Lusztig varieties using double Grothendieck polynomials, connecting geometry with algebraic combinatorics.

## Key findings

- Explicit double Grothendieck polynomial formulas derived
- Closure classes viewed as degeneracy loci of vector bundle morphisms
- Bridges between geometric and algebraic descriptions of Deligne-Lusztig varieties

## Abstract

In this paper we express the class of the structure sheaves of the closures of Deligne--Lusztig varieties as explicit double Grothendieck polynomials in the first Chern classes of appropriate line bundles on the ambient flag variety. This is achieved by viewing such closures as degeneracy loci of morphisms of vector bundles.