This paper constructs central elements in the center of the vertex algebra for orthosymplectic Lie superalgebras, suggesting new insights into commutative properties.
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.
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Molev et al. (2025) studied this question.
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