Transformation Groups

, Volume 1, Issue 1–2, pp 99–126 | Cite as

Quantum immanants and higher Capelli identities

  • Andrei Okounkov


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.


Irreducible Character Quantum Immanants Characterization Theorem High Term Standard Tableau 
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© Birkhäuser Boston 1996

Authors and Affiliations

  • Andrei Okounkov
    • 1
  1. 1.Institute for Problems of Information TransmissionMoscowRussia

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