The multiplicity of the Steinberg representation of in the symmetric algebra

Authors:
N. J. Kuhn and S. A. Mitchell

Journal:
Proc. Amer. Math. Soc. **96** (1986), 1-6

MSC:
Primary 20G40; Secondary 20G05, 20J06, 55R40, 55S10

DOI:
https://doi.org/10.1090/S0002-9939-1986-0813797-6

MathSciNet review:
813797

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Abstract: Let denote the symmetric algebra on the standard -dimensional representation of . *The multiplicity series* in for the Steinberg representation St of is determined. This series is defined by where is the multiplicity of St in the th symmetric power . We show that , where . The proof involves a general property of Tits buildings and a computation of the invariants in of the parabolic subgroups of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0813797-6

Article copyright:
© Copyright 1986
American Mathematical Society