Journal of Lie Theory, Vol. 10, No. 2, pp. 463-489 (2000)

Capelli elements for the orthogonal Lie algebras

Minoru Itoh

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

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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