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Intertwining ladder representations for SU(p, q) into Dolbeault cohomology

  • John D. Lorch
  • Lisa A. Mantini
  • Jodie D. Novak
Chapter
Part of the Progress in Mathematics book series (PM, volume 220)

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.

1991 Mathematics Subject Classification:

Primary 22E46, 22E70 Secondary 32L25, 32M15, 58G05, 81R05, 81R25 

Key words

Penrose transform ladder representations Dolbeault cohomology integral transform intertwining operator double fibration transform unitary representation 

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • John D. Lorch
    • 1
  • Lisa A. Mantini
    • 2
  • Jodie D. Novak
    • 3
  1. 1.Department of MathematicsBall State UniversityMuncieUSA
  2. 2.Department of MathematicsOklahoma State UniversityStillwaterUSA
  3. 3.Department of Mathematical SciencesUniversity of Northern ColoradoGreeleyUSA

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