A new formula for Pfaffian-type Segal-Sugawara vector

Abstract

A combinatorial formula for Pfaffian for the universal enveloping algebra of the affine Kac - Moody algebra of even orthogonal Lie algebra is proved. It allows easily to compute the image of this Segal-Sugawara vector under the Harish-Chandra homomorphism and to deduce formulas for classical Pfaffian of universal enveloping algebra of the even orthogonal Lie algebra.

14 pages

References in corpus (2)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• On higher order Sugawara operators

Cited by in corpus (1)

• Segal-Sugawara vectors for the Lie algebra of type $G_2$