Cauchy Formulas and Billey's Formulas for Generalized Grothendieck polynomials

2021/06/12 by Rui Xiong, Xiong, Rui
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.2106.06872

a part of master thesis of the author

arxiv created 2021/06/12 · arxiv updated 2021/06/15

Abstract

We study the generalized double β-Grothendieck polynomials for all types. We study the Cauchy formulas for them. Using this, we deduce the K-theoretic version of the comodule structure map α^*: K(G/B)→ K(G)⊗ K(G/B) induced by the group action map for reductive group G and its flag variety G/B. Furthermore, we give a combinatorial formula to compute the localization of Schubert classes as a generalization of Billey's formula.

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