Bender-Knuth involutions for types B and C
Combinatorics
2025-09-23 v3 Representation Theory
Abstract
We show that the combinatorial definitions of King and Sundaram of the symmetric polynomials of types B and C are indeed symmetric, in the sense that they are invariant by the action of the Weyl groups. Our proof is combinatorial and inspired by Bender and Knuth's classic involutions for type A.
Cite
@article{arxiv.2311.10659,
title = {Bender-Knuth involutions for types B and C},
author = {Álvaro Gutiérrez},
journal= {arXiv preprint arXiv:2311.10659},
year = {2025}
}
Comments
11 pages + 1 page (addendum). Added a detropicalized proof by Darij Grinberg