English

The GL_n(q)-module structure of the symmetric algebra around the Steinberg module

Representation Theory 2011-05-20 v2 Group Theory

Abstract

We determine the graded composition multiplicity in the symmetric algebra S(V) of the natural GL_n(q)-module V, or equivalently in the coinvariant algebra of V, for a large class of irreducible modules around the Steinberg module. This was built on a computation, via connections to algebraic groups, of the Steinberg module multiplicity in a tensor product of S(V) with other tensor spaces of fundamental weight modules.

Keywords

Cite

@article{arxiv.1012.0406,
  title  = {The GL_n(q)-module structure of the symmetric algebra around the Steinberg module},
  author = {Jinkui Wan and Weiqiang Wang},
  journal= {arXiv preprint arXiv:1012.0406},
  year   = {2011}
}

Comments

v2, 21 pages, minor changes, some typos fixed and updated references, Adv. in Math. (to appear)