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2011

Kirillov's formula and Guillemin-Sternberg conjecture

Duflo, Michel, Vergne, Michèle

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Let G be a connected reductive real Lie group, and H a compact connected subgroup.

Harish-Chandra associates to a regular coadjoint admissible orbit M of G some unitary representations of G.
Using the character formula for these representations, we show that the multiplicities of the restriction to H can be computed, under a suitable properness assumption, in terms of the fibers of the restriction map from M to the dual of the Lie algebra of H.
In particular, this gives an alternate proof of a result of Paradan.

Kirillov's formula and Guillemin-Sternberg conjecture · Around

Built on

W. Rossmann, Kirillov’s character formula for reductive Lie groups
1978
Earlier work this paper cites.
J. J. Duistermaat, G. J. Heckman, On the variation in the cohomology of the symplectic form on the reduced phase space
1982
Earlier work this paper cites.
M. Duflo, G. J. Heckman, M. Vergne, Projections d’orbites, formule de Kirillov et formule de Blattner
1984
Earlier work this paper cites.

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C. De Concini, C. Procesi, M. Vergne, Box splines and the equivariant index theorem
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P.-E. Paradan, Spin-quantization commutes with reduction
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Then

P.-E. Paradan, S p i n c Spin_{c} quantization and the K-multiplicities of the discrete series
2003
Later among the works it cites.
M. Duflo, Construction de représentations unitaires d’un groupe de Lie
2011
Closest in time.

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