Construction of double Grothendieck polynomials of classical types using IdCoxeter algebras

TL;DR

This paper constructs simplified double Grothendieck polynomials for classical types, linking them to existing polynomials and providing geometric and combinatorial interpretations.

Contribution

It introduces a new, simpler construction of double Grothendieck polynomials for classical types and connects them with known polynomials and geometric localization.

Findings

Constructed simplified double Grothendieck polynomials for classical types.

Identified these polynomials with previously defined polynomials for maximal Grassmannian permutations.

Provided geometric and combinatorial formulas for these polynomials.

Abstract

We construct double Grothendieck polynomials of classical types which are essentially equivalent to but simpler than the polynomials defined by A.N.Kirillov in arXiv:1504.01469 and identify them with the polynomials defined by T.Ikeda and H.Naruse in Adv. Math.(2013) for the case of maximal Grassmannian permutations. We also give geometric interpretation of them in terms of algebraic localization map and give explicit combinatorial formulas.