## Branching laws for square integrable representations.(English)Zbl 1196.22009

The authors study square integrable representations of a real reductive Lie group $$G$$. They show that for a square integrable representation, its restriction to a closed connected reductive subgroup $$H$$ is admissible if and only if the restriction to the intersection $$L$$ of $$H$$ with a maximal compact subgroup is admissible. This gives a strategy for the computation of the multiplicities in the restriction to $$H$$ for the admissible case via the multiplicities in the restriction to $$L$$. The authors give nice formulae (in terms of partition functions) for the multiplicities in the restriction to $$L$$ under some natural additional assumptions. Finally, the authors also consider the semi-classical analogue of these results for coadjoint orbits.

### MSC:

 22E46 Semisimple Lie groups and their representations 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 05E15 Combinatorial aspects of groups and algebras (MSC2010)
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### References:

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