Spinc-quantization and the K-multiplicities of the discrete series
By P. Paradan. 2001
57 citations recorded by the source corpus.
Abstract In the 70s, W. Schmid has shown that the representations of the discrete series of a real semi-simple Lie group G could be realized as the quantization of elliptic coadjoint orbits. In this paper we show that such orbits, equipped with the Hamiltonian action of a maximal compact subgroup K⊂G, are non-compact examples where the philosophy of Guillemin–Sternberg—Quantization commutes with reduction—applies. If H O is a representation of the discrete series of G associated to a coadjoint orbit O , we express the K-multiplicities of H O in terms of Spinc-index on symplectic reductions of O .
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2018201c3883898251bf32febbec603874af746c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
Citations in the corpus
- Index of transversally elliptic operators (2008, background): “The restriction to the maximal compact subgroup K of a representation of the discrete series of a real reductive group are indices of transversally elliptic operators [ 15 ].”
- Geometric quantization for proper moment maps: the Vergne conjecture (2008, methodology): “3], et des cas particuliers de cette conjecture ont été démontrés par Paradan [11,12], dans le cadre des séries discrètes.”
- Applications of Equivariant Cohomology (2006, background): “map µ for the K-action on N is the projection Gλ → k∗ and the set C of zeroes of the Kirwan vector field κ is easy to compute in this case: it consists of the compact orbit K · λ. Theorem 14. (Paradan [39]) The character of the discrete series ΘG(λ) restricted to K is the index of the transversally e”