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

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

2010-12-02

arxiv.org/abs/1012.0406v2

Advances in Mathematics 227 (2011) 1562-1584

Mathematics

Representation Theory

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

Scientific paper

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.

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