Pfaffian-type Sugawara operators

A. I. Molev

Abstract

We show that the Pfaffian of a generator matrix for the affine Kac-Moody algebra \(\hat o_{2n}\) is a Segal-Sugawara vector. Together with our earlier construction involving the symmetrizer in the Brauer algebra, this gives a complete set of Segal-Sugawara vectors in type \(D\).