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), 16
MSC:
Primary 20G40; Secondary 20G05, 20J06, 55R40, 55S10
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:
http://dx.doi.org/10.1090/S00029939198608137976
PII:
S 00029939(1986)08137976
Article copyright:
© Copyright 1986
American Mathematical Society
