Translator Disclaimer
2019 A comment on the combinatorics of the vertex operator $\Gamma _{(t|X)}$
Mercedes Helena Rosas
Rocky Mountain J. Math. 49(7): 2281-2295 (2019). DOI: 10.1216/RMJ-2019-49-7-2281

Abstract

The Jacobi--Trudi identity associates a symmetric function to any integer sequence. Let $\Gamma _{(t|X)}$ be the vertex operator defined by $\Gamma _{(t|X)} s_\alpha =\sum _{n \in \mathbb{Z} } s_{(n,\alpha )} [X] t^n$. We provide a combinatorial proof for the identity $\Gamma _{(t|X)} s_\alpha = \sigma [tX] s_{\alpha }[x-1/t] $ due to Thibon et al. We include an overview of all the combinatorial ideas behind this beautiful identity, including a combinatorial description for the expansion of $s_{(n,\alpha )} [X] $ in the Schur basis, for any integer value of $n$.

Citation

Download Citation

Mercedes Helena Rosas. "A comment on the combinatorics of the vertex operator $\Gamma _{(t|X)}$." Rocky Mountain J. Math. 49 (7) 2281 - 2295, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2281

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152865
MathSciNet: MR4039970
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2281

Subjects:
Primary: Priamry:
Secondary: 05E10

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 7 • 2019
Back to Top