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

2012/01/15 by Zhi Chen, Chen, Zhi
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1201.3057

arxiv created 2012/01/15 · arxiv updated 2012/01/17

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 P_n(Y,q). A recurrence relation is also given which makes it easy to carry out the computation.

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