We consider some remarkable central elements of the universal enveloping algebraU(gl(n)) which we call quantum immanants. We express them in terms of generatorsE ij ofU(gl(n)) and as differential operators on the space of matrices These expressions are a direct generalization of the classical Capelli identities. They result in many nontrivial properties of quantum immanants.
KeywordsIrreducible Character Quantum Immanants Characterization Theorem High Term Standard Tableau
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