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An extension of the Borel-Weil construction to the quantum groupU q (n)

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Abstract

The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum groupU q(n). Thisq-BW construction uses a recursion procedure forU q(n) in which the fiber of the bundle carries an irrep ofU q(n−1)×U q(1) with sections that are holomorphic functions in the homogeneous spaceU q(n)/U q(n−1)×U q(1). Explicit results are obtained for theU q(n) irreps and for the related isomorphism of quantum group algebras.

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Authors and Affiliations

  1. Department of Physics, Duke University, 27706, Durham, NC, USA

    L. C. Biedenharn

  2. Faculty of Science, Northern Territory University, 0811, Casuarina, NT, Australia

    M. A. Lohe

Authors
  1. L. C. Biedenharn
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  2. M. A. Lohe
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Communicated by J. Fröhlich

Supported in part by the National Science Foundation, No. PHY-9008007

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Biedenharn, L.C., Lohe, M.A. An extension of the Borel-Weil construction to the quantum groupU q (n). Commun.Math. Phys. 146, 483–504 (1992). https://doi.org/10.1007/BF02097014

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