Type: Seminar

Distribution: World

Expiry: 5 Aug 2011

Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

The Algebra Seminar on Friday 5 August will be given by Alexander Molev. --------------------------------------------------------------------------- Speaker: Alexander Molev (University of Sydney) Date: Friday 5 August Time: 12.05-12.55pm Venue: Carslaw 175 Title: Feigin-Frenkel center for classical types Abstract: For each simple Lie algebra g consider the corresponding affine vertex algebra V(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev’s discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras V(g) associated with the simple Lie algebras g of types B, C and D. The construction relies on the Schur-Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra sl(2) in the context of the Howe duality. ----------------------------------------------------------------------------