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arXiv · 1012.0406

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

Jinkui Wan·Weiqiang Wang
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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.

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Jinkui Wan, Weiqiang Wang. 2010-12-02. The GL_n(q)-module structure of the symmetric algebra around the Steinberg module. https://arxiv.org/abs/1012.0406

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