On Segal--Sugawara vectors and Casimir elements for classical Lie algebras

Abstract

We consider the centers of the affine vertex algebras at the critical level associated with simple Lie algebras. We derive new formulas for generators of the centers in the classical types. We also give a new formula for the Capelli-type determinant for the symplectic Lie algebras and calculate the Harish-Chandra images of the Casimir elements arising from the characteristic polynomial of the matrix of generators of each classical Lie algebra.

arXiv comment21 pages, extended version with more detailed expressions for Segal--Sugawara vectors

References in corpus (7)

• Shifted Schur Functions
• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• On higher order Sugawara operators
• Feigin-Frenkel center in types B, C and D
• Yangian characters and classical W-algebras
• Segal-Sugawara vectors for the Lie algebra of type $G_2$
• Casimir elements from the Brauer-Schur-Weyl duality

Cited by in corpus (2)

• Segal-Sugawara vectors for orthosymplectic Lie superalgebras
• On the quantum argument shift method