A decomposition formula for representations
Keyword(s):
Know How
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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.
1988 ◽
Vol 40
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pp. 633-648
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1978 ◽
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2012 ◽
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pp. 673-688
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pp. 149-167
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2021 ◽
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pp. 606-643