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University of Sydney Algebra Seminar

Alexander Molev

Friday 22 March, 12-1pm, Place: Carslaw 175

Harish-Chandra images of quantum Gelfand invariants

By a landmark work of Reshetikhin, Takhtajan and Faddeev (1989), the quantized enveloping algebras contain families of central elements analogous to the Gelfand invariants. The eigenvalues of the Gelfand invariants in irreducible highest weight modules are known since 1966, but the problem of finding their quantum analogues has remained open. We give a solution for type $A$ by using a Liouville formula for the associated quantum affine algebra relating two families of central elements. This is a joint work with Naihuan Jing and Ming Liu.