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arXiv · 1201.3057

A Plethysm formula on the characteristic map of induced linear characters from $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$

Zhi Chen
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Abstract

This paper gives a plethysm formula on the characteristic map of the induced linear characters from the unipotent upper-triangular matrices $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$, the general linear group over finite field $\mathbb F_q$. The result turns out to be a multiple of a twisted version of the Hall-Littlewood symmetric functions $\tilde{P}_n(Y,q)$. A recurrence relation is also given which makes it easy to carry out the computation.

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Zhi Chen. 2012-01-15. A Plethysm formula on the characteristic map of induced linear characters from $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$. https://arxiv.org/abs/1201.3057

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