Abstract
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.
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Lorch, J.D., Mantini, L.A., Novak, J.D. (2004). Intertwining ladder representations for SU(p, q) into Dolbeault cohomology. In: Delorme, P., Vergne, M. (eds) Noncommutative Harmonic Analysis. Progress in Mathematics, vol 220. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8204-0_14
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DOI: https://doi.org/10.1007/978-0-8176-8204-0_14
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