On a q-Identity Arising from the Dimension of a Representation of GL(n) over a Finite Field

2016/11/20 by Ofir Gorodetsky, Gorodetsky, Ofir, Zahi Hazan +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1611.06502

12 pages. Comments are welcome

arxiv created 2016/11/20 · arxiv updated 2016/11/22

Abstract

The present paper proves a q-identity, which arises from a representation π_N,ψ of GL_n(\mathbbF_q). This identity gives a significant simplification for the dimension of π_N,ψ, which allowed the second author to obtain a description of the representation.

Related

• Representations of GL₂(\Fq) and SL₂(\Fq), and some remarks about GL_n(\Fq)
• Gelfand-Kirillov dimension of representations of GL_n over a non-archimedean local field
• Harmonic Analysis on GL(n) over Finite Fields
• Symmetrization of representations of GL_N
• Rational representations of GL₂