Algebra Seminar: Molev -- Feigin-Frenkel center for classical types

The Algebra Seminar on Friday 5 August will be given by Alexander Molev.  

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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.
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