Kirillov's formula and Guillemin-Sternberg conjecture

Details Kirillov's formula and Guillemin-Sternberg conjecture Kirillov's formula and Guillemin-Sternberg conjecture

2011-10-05

arxiv.org/abs/1110.0987v1

Mathematics

Representation Theory

7 pages

Scientific paper

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.

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