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Journal of Lie Theory 24 (2014), No. 2, 529--543
Copyright Heldermann Verlag 2014

A New Formula for the Pfaffian-Type Segal-Sugawara Vector

Natasha Rozhkovskaya
Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66502, U.S.A.


\def\o{{\frak o}} A combinatorial formula for the Pfaffian of the universal enveloping algebra $U(\widehat{\o}_{2n})$ of the affine Kac-Moody algebra $\widehat{\o}_{2n}$ is proved. It allows us easily to compute the image of the Segal-Sugawara vector under the Harish-Chandra homomorphism and to deduce formulas for the classical Pfaffian of the universal enveloping algebra $U(\o_{2n})$ of the even orthogonal Lie algebra.

Keywords: Pfaffian, affine orthogonal Lie algebra, Feigin-Frenkel center, Harish-Chandra homomorphism.

MSC: 17B35, 17B67

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