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.

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Molev, A.I. On Segal–Sugawara vectors and Casimir elements for classical Lie algebras. Lett Math Phys 111, 8 (2021). https://doi.org/10.1007/s11005-020-01344-3

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Keywords

  • Affine Kac-Moody algebra
  • Feigin-Frenkel center
  • Harish-Chandra isomorphism
  • Capelli determinant

Mathematics Subject Classification

  • 17B69
  • 17B35