Set-valued domino tableaux and shifted set-valued domino tableaux

Maas-Gariépy, Florence; Patrias, Rebecca

doi:10.2140/involve.2020.13.721

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Set-valued domino tableaux and shifted set-valued domino tableaux

Florence Maas-Gariépy and Rebecca Patrias

Vol. 13 (2020), No. 5, 721–746

DOI: 10.2140/involve.2020.13.721

Abstract

We prove $K$ -theoretic and shifted $K$ -theoretic analogues of the bijection of Stanton and White between domino tableaux and pairs of semistandard tableaux. As a result, we obtain product formulas for certain pairs of stable Grothendieck polynomials and certain pairs of $K$ -theoretic $Q$ -Schur functions.

Keywords

set-valued tableaux, Schur functions, stable Grothendieck polynomials, Lagrangian Grassmannian

Mathematical Subject Classification 2010

Primary: 05E05

Milestones

Received: 22 July 2018

Revised: 23 February 2020

Accepted: 10 August 2020

Published: 5 December 2020

Communicated by Kenneth S. Berenhaut

Authors

Florence Maas-Gariépy
Laboratoire de Combinatoire et d’Informatique Mathématique Université du Québec à Montréal Montréal, QC Canada

Rebecca Patrias
Laboratoire de Combinatoire et d’Informatique Mathématique Université du Québec à Montréal Montréal, QC Canada

Vol. 13, No. 5, 2020