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Journal of Lie Theory, Vol. 10, No. 2, pp. 463-489 (2000)
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Capelli elements for the orthogonal Lie algebras

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Minoru Itoh

Department of Mathematics

Faculty of Science

Kyoto University

Kyoto 606-8502, Japan

minoru@kusm.kyoto-u.ac.jp

**Abstract:** For the central elements in the universal enveloping algebra of the orthogonal Lie algebra given by R. Howe and T. Umeda, Newton type and Cayley-Hamilton type identities are given, and their images under the Harish-Chandra homomorphism are determined. These results show that these central elements can be regarded as the counterparts of the Capelli elements. The calculation of the images under the Harish-Chandra homomorphism clearly reveals the fact that these central elements coincide with those given with the Sklyanin determinant.

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