Twisted Dickson-Mui invariants and the Steinberg module multiplicity
Representation Theory
2015-05-19 v2 Algebraic Topology
Abstract
We determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GL_n(q) acting on the tensor product of the symmetric algebra and the exterior algebra of the natural GL_n(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GL_n(q) in the tensor product of the symmetric algebra and the exterior algebra of V, twisted by an arbitrary determinant power.
Cite
@article{arxiv.1009.0414,
title = {Twisted Dickson-Mui invariants and the Steinberg module multiplicity},
author = {Jinkui Wan and Weiqiang Wang},
journal= {arXiv preprint arXiv:1009.0414},
year = {2015}
}
Comments
v2, 15 pages, minor changes, some typos fixed and references added, to appear in Math. Proc. Camb. Phil. Soc