An extension of the Borel-Weil construction to the quantum groupU q (n) |
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| Authors: | L. C. Biedenharn M. A. Lohe |
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| Affiliation: | (1) Department of Physics, Duke University, 27706 Durham, NC, USA;(2) Faculty of Science, Northern Territory University, 0811 Casuarina, NT, Australia |
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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 groupUq(n). Thisq-BW construction uses a recursion procedure forUq(n) in which the fiber of the bundle carries an irrep ofUq(n–1)×Uq(1) with sections that are holomorphic functions in the homogeneous spaceUq(n)/Uq(n–1)×Uq(1). Explicit results are obtained for theUq(n) irreps and for the related isomorphism of quantum group algebras.Supported in part by the National Science Foundation, No. PHY-9008007 |
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