K-theoretic Poirier-Reutenauer bialgebra

Abstract

We use the K-Knuth equivalence of Buch and Samuel to define a K-theoretic analogue of the Poirier-Reutenauer Hopf algebra. As an application, we rederive the K-theoretic Littlewood-Richardson rules of Thomas and Yong and of Buch and Samuel.

arXiv comment25 pages

References in corpus (2)

• K-theory of minuscule varieties
• The direct sum map on Grassmannians and jeu de taquin for increasing tableaux

Cited by in corpus (3)

• Duality and deformations of stable Grothendieck polynomials
• Shifted Hecke insertion and the K-theory of OG(n,2n+1)
• K-Knuth Equivalence for Increasing Tableaux