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A decomposition formula for representations*

Published online by Cambridge University Press:  22 January 2016

George Kempf
George Kempf*
Affiliation:
Department of Mathematics, The Johns Hopkins University Baltimore, Maryland 21218 U.S.A.
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Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 107 , September 1987 , pp. 63 - 68
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

Footnotes

*

Partially supported by NSF Grant #MPS75-05578.

References

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