Segal-Sugawara vectors for orthosymplectic Lie superalgebras

TL;DR

This paper constructs explicit elements of the centre of the affine vertex algebra at critical level for orthosymplectic Lie superalgebras, providing new proofs for classical central element formulas using an extended Brauer-type algebra.

Contribution

It introduces a novel explicit construction of central elements for orthosymplectic Lie superalgebras and offers a new proof of known formulas through an extended Brauer-type algebra.

Findings

Explicit formulas for central elements derived

New proof for orthogonal and symplectic Lie algebras

Introduction of an extended Brauer-type algebra

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.