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## A $q$-multinomial expansion of LLT coefficients and plethysm multiplicities

### Abstract

Lascoux, Leclerc and Thibon\cite{LLT} introduced a family of symmetric polynomials, called LLT polynomials. We prove a $q$-multinomial expansion of the coefficients of LLT polynomials in the case where $\boldsymbol{\mu} = \underbrace{(\mu,...,\mu)}_{n}$ and define a $q$-analog of a sum of the plethysm multiplicities

Topics: Mathematics - Representation Theory, Mathematics - Combinatorics
Year: 2011
OAI identifier: oai:arXiv.org:1104.4870