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Lie Groups Quantum Mathematics Seminar

The Capelli eigenvalue problem for Lie superalgebras

Siddhartha Sahi, Rutgers University

Location:  HILL 705
Date & time: Friday, 08 September 2017 at 12:00PM - 1:00PM

  • Abstract:  The Tits-Kantor-Koecher (TKK) construction attaches a simple Lie algebra to a simple Jordan algebra. In this setting one has a Jordan "norm" that generalizes the determinant, and a family of invariant differential operators generalizing the Capelli operators of classical invariant theory. In the early 1990s Bert Kostant and I studied the eigenvalues of these generalized Capelli operators, and a few years later Friedrich Knop and I discovered a surprising connection to Macdonald polynomials.  
  • It turns out that these ideas have analogs for Lie superalgebras, although there are several subtle issues and new phenomena. I will describe a number of recent results in this direction, which have been obtained in joint work with Hadi Salmasian, Alexander Alldridge, and Vera Serganova.

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