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Explicit realization of irreducible representations of classical compact lie groups in the spaces of sections of line bundles

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Abstract

We use the Borel-Weil scheme for the construction of irreducible representations of compact Lie groups in the spaces of holomorphic sections of line bundles over homogeneous manifolds. We find the explicit form of the space of sections and construct an invariant scalar product. We show that the space of holomorphic sections locally satisfies the Zhelobenko indicator system.

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Authors and Affiliations

  1. Institute for Theoretical Physics, Ukrainian Academy of Sciences, Kiev

    P. I. Golod & T. V. Skrypnyk

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  1. P. I. Golod
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  2. T. V. Skrypnyk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1316–1323, October, 1998.

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Golod, P.I., Skrypnyk, T.V. Explicit realization of irreducible representations of classical compact lie groups in the spaces of sections of line bundles. Ukr Math J 50, 1504–1512 (1998). https://doi.org/10.1007/BF02513499

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  • DOI: https://doi.org/10.1007/BF02513499

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