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

L.C. Biedenharn, Max A. Lohe

    Research output: Contribution to journalComment/debate

    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 group U q(n). This q-BW construction uses a recursion procedure for U q(n) in which the fiber of the bundle carries an irrep of U q(n-1)×U q(1) with sections that are holomorphic functions in the homogeneous space U q(n)/U q(n-1)×U q(1). Explicit results are obtained for the U q(n) irreps and for the related isomorphism of quantum group algebras.
    Original languageEnglish
    Pages (from-to)483-504
    Number of pages22
    JournalCommunications in Mathematical Physics
    Volume146
    Issue number3
    DOIs
    Publication statusPublished - 1992

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