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Capelli Identities for the dual pair (O M ,Sp N )

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Abstract.

Analogues of the Capelli identity are given from the viewpoint of dual pair theory. The Capelli identity is a famous formula in the invariant theory, and can be regarded as an explicit description of a correspondence of invariant differential operators associated to the dual pair (GL r ,GL s ). The main results are Capelli type identities in this sense for the dual pair (O M ,Sp N ).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan

    Minoru Itoh

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  1. Minoru Itoh
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Correspondence to Minoru Itoh.

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Mathematics Subject Classification (2000): 17B35, 16S32, 15A15, 15A72.

Partially supported by JSPS Research Fellowships for Young Scientists.

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Itoh, M. Capelli Identities for the dual pair (O M ,Sp N ). Math. Z. 246, 125–154 (2004). https://doi.org/10.1007/s00209-003-0591-2

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  • DOI: https://doi.org/10.1007/s00209-003-0591-2

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