2023/01/30 by Jakub Koncki, Koncki, Jakub, Andrzej Weber +1 · 1 citation
Mathematics · #14M15 #14N15 #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Primary 14C17 #Secondary 19L47
paper · pdf · doi:10.48550/arxiv.2301.12746
openalex publication_date 2023/01/30 · openalex created_date 2023/02/01 · openalex updated_date 2026/07/28
Let G be a linear semisimple algebraic group and B its Borel subgroup. Let \mathbbT⊂ B be the maximal torus. We study the inductive construction of Bott-Samelson varieties to obtain recursive formulas for the twisted motivic Chern classes of Schubert cells in G/B. To this end we introduce two families of operators acting on the equivariant K-theory K_\mathbbT(G/B)[y], the right and left Demazure-Lusztig operators depending on a parameter. The twisted motivic Chern classes coincide (up to normalization) with the K-theoretic stable envelopes. Our results imply wall-crossing formulas for a change of the weight chamber and slope parameters. The right and left operators generate a twisted double Hecke algebra. We show that in the type A this algebra acts on the Laurent polynomials. This action is a natural lift of the action on K_\mathbbT(G/B)[y] with respect to the Kirwan map. We show that the left and right twisted Demazure-Lusztig operators provide a recursion for twisted motivic Chern classes of matrix Schubert varieties.