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Capelli identities for classical Lie algebras

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Abstract.

We extend the Capelli identity from the Lie algebra \(\frak{gl}_N\) to the other classical Lie algebras \(\frak{so}_N\) and \(\frak{sp}_N\). We employ the theory of reductive dual pairs due to Howe.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, Australia (e-mail: alexm@maths.usyd.edu.au) , , , , , , AU

    Alexander Molev

  2. Department of Mathematics, University of York, York YO1 5DD, England (e-mail: mln1@york.ac.uk) , , , , , , GB

    Maxim Nazarov

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  1. Alexander Molev
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  2. Maxim Nazarov
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Received: 12 February 1997 / in revised form: 24 July 1998

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Molev, A., Nazarov, M. Capelli identities for classical Lie algebras. Math Ann 313, 315–357 (1999). https://doi.org/10.1007/s002080050263

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  • DOI: https://doi.org/10.1007/s002080050263

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