Segal-Sugawara vectors for orthosymplectic Lie superalgebras

Alexander Molev, Madeline Nurcombe

Abstract

We consider the centre of the affine vertex algebra at the critical level associated with the orthosymplectic Lie superalgebra. It is well-known that the centre is a commutative superalgebra, and we construct a family of its elements in an explicit form. In particular, this gives a new proof of the formulas for the central elements for the orthogonal and symplectic Lie algebras. Our arguments rely on the properties of a new extended Brauer-type algebra.

Keywords: Segal-Sugawara vectors, Feigin-Frenkel centre, orthosymplectic, affine Lie superalgebras, representation theory.

AMS Subject Classification: Primary 17B35; secondary 17B67, 17B65.