Young Basis, Wick Formula, and Higher Capelli Identities
Abstract
We prove Capelli type identities which involve the whole universal enveloping algebra U(gl(n)) and matrix elements of irreducible representations of the symmetric group. These identities generalize higher Capelli identities for the center of U(gl(n)) introduced in the author's paper Ok. The main role in the proof play the Jucis-Murphy elements.
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