A row analogue of Hecke column insertion

TL;DR

This paper introduces a novel row insertion algorithm for decreasing and increasing tableaux, extending Hecke column insertion, and connects it to stable Grothendieck functions, enriching combinatorial representation theory.

Contribution

It presents a new row insertion algorithm that generalizes Edelman-Greene and Hecke column insertion, maintaining bijectivity and Hecke equivalence.

Findings

The algorithm is bijective and respects Hecke equivalence.

It recovers expansions of stable Grothendieck functions into Grassmannian stable Grothendieck functions.

Provides a combinatorial framework for these functions.

Abstract

We introduce a new row insertion algorithm on decreasing tableaux and increasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivial variation of Hecke column insertion which generalizes EG column insertion. Similar to Hecke column insertion, our row insertion is bijective and respects Hecke equivalence, and therefore recovers the expansions of stable Grothendieck functions into Grassmannian stable Grothendieck functions.