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Algebra Seminar
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Minoru Itoh
University of Kyoto

Capelli identities for reductive dual pairs

Friday 5th September, 12:05-12:55pm, Carslaw 373.

We present analogues of the Capelli identity from the viewpoint of dual pair theory, and complete the list of Capelli type identities written in terms of determinants and permanents for all the irreducible reductive dual pairs in the complex symplectic group and the complex orthogonal group. These Capelli type identities describe a natural correspondence between the "centers" of the two universal enveloping algebras and an algebra of invariant operators.