Segal-Sugawara vectors for orthosymplectic Lie superalgebras

2025/07/30 by Alexander Molev, Molev, Alexander, Madeline Nurcombe +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2507.22738

openalex publication_date 2025/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Interpolating Feigin-Frenkel Duality at the Critical Level to Matrices of Complex Size
• Center of affine \mathfraksl_2|1 at the critical level
• The Schur-Weyl duality and Invariants for classical Lie superalgebras
• Symmetrisation and the Feigin-Frenkel centre
• Invariants of the orthosymplectic Lie superalgebra and super Pfaffians
• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence

Related

• The centre of the modular affine vertex algebra
• The second fundamental theorem of invariant theory for the orthosymplectic supergroup
• The first fundamental theorem of invariant theory for the orthosymplectic supergroup
• Tensor product representations for orthosymplectic Lie superalgebras
• Central extensions of generalized orthosymplectic Lie superalgebras