Dirac cohomology, \(K\)-characters and branching laws (Q2856609)
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scientific article; zbMATH DE number 6220928
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dirac cohomology, \(K\)-characters and branching laws |
scientific article; zbMATH DE number 6220928 |
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30 October 2013
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Dirac cohomology
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Littlewood restriction formula
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branching laws
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Dirac cohomology, \(K\)-characters and branching laws (English)
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The authors prove a generalization of the Littlewood restriction formula in terms of the Dirac cohomology using a character formula of irreducible unitary lowest weight modules. The proofs depend heavily on the Howe duality [\textit{R. Howe}, Trans. Am. Math. Soc. 313, No. 2, 539--570 (1989; Zbl 0674.15021)] and use the notion of see-saw dual pairs introduced by \textit{S. S. Kudla} [Prog. Math. 46, 244--268 (1984; Zbl 0549.10017)]. The authors also relate their formula to that of \textit{T. J. Enright} and \textit{J. F. Willenbring} [Ann. Math. (2) 159, No. 1, 337--375 (2004; Zbl 1087.22011)] by passing from the lowest weight modules to the highest weight modules via an automorphism of the group.
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