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27 April 2024

» arxiv » 1012.0406

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The GL_n(q)-module structure of the symmetric algebra around the Steinberg module
Jinkui Wan ; Weiqiang Wang ;
Date:	2 Dec 2010
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.
Source:	arXiv, 1012.0406
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