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Correspondences of the Gelfand invariants in reductive dual pairs

Published online by Cambridge University Press:  09 April 2009

Minoru Itoh
Affiliation:
Department of Mathematics Faculty of Science Kyoto UniversityKyoto 606-8502Japan e-mail: minoru@kusm.kyoto-u.ac.jp
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Abstract

For each complex reductive dual pair introduced by R. Howe, this paper presents a formula for the central elements of the universal enveloping algebras given by I. M. Gelfand. This formula provides an explicit description of the correspondence between the ‘centers’ of the two universal enveloping algebras.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

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