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

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

2011-04-26

arxiv.org/abs/1104.4870v1

Mathematics

Representation Theory

Scientific paper

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.

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