Intertwining ladder representations for SU(p, q) into Dolbeault cohomology
The positive spin ladder representations for G = SU(p, q)may be realized in a Fock space, in Dolbeault cohomology over G/S(U(p, q−1) × U(1)), and as certain holomorphic sections of a vector bundle over G/S(U(p) × U(q)). A Penrose transform, also referred to as a double fibration transform, intertwines the Dolbeault model into the vector bundle model. By passing through the Fock space realization of the ladder representations, we invert the Penrose transform, and thus intertwine the ladder representations into Dolbeault cohomology.
1991 Mathematics Subject Classification:Primary 22E46, 22E70 Secondary 32L25, 32M15, 58G05, 81R05, 81R25
Key wordsPenrose transform ladder representations Dolbeault cohomology integral transform intertwining operator double fibration transform unitary representation
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- [BE]R. Baston and M. Eastwood, The Penrose Transform, Clarendon Press, 1989.Google Scholar
- [H]L.K. Hua, Harmonic Analysis of Functions of Several Complex Variables, Amer. Math. Soc., Providence, RI, 1963.Google Scholar
- [LA]M. Kashiwara and W. Schmid, Quasi-equivariant D-modules, equivariant derived category, and representations of reductive Lie groups, in Lie Theory and Geometry, Progr. Math. vol. 123, Birkhäuser, Boston, 1994, 457–488.Google Scholar
- [Z]R. Zierau, Representations in Dolbeault cohomology, in Representation Theory of Lie Groups, IAS/Park City Mathematics Series vol. 8, Amer. Math. Soc., Providence, RI, 2000, 91–146.Google Scholar