## 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 $$D$$.

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 Friday, August 19, 2011