Mathematical Research Letters

Volume 21 (2014)

Number 2

A proof of $K$-theoretic Littlewood-Richardson rules by Bender-Knuth-type involutions

Pages: 333 – 339

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n2.a10

Authors

Takeshi Ikeda (Department of Applied Mathematics, Okayama University of Science, Okayama, Japan)

Tatsushi Shimazaki (Department of Applied Mathematics, Okayama University of Science, Okayama, Japan)

Abstract

The $K$-theoretic Littlewood-Richardson rule due to A. Buch describes the product structure constants for the Grothendieck polynomials of Grassmannian type. We present a simple self-contained proof of the rule by generalizing Stembridge’s cancelation argument which was applied for the classical Littlewood-Richardson rule.

2010 Mathematics Subject Classification

05E05, 14M15, 19E08

Full Text (PDF format)

Published 1 August 2014

November 7, 2014: Author name spelling corrected from “Takehi” to “Takeshi”.