
Journal of Lie Theory 24 (2014), No. 2, 529543 Copyright Heldermann Verlag 2014 A New Formula for the PfaffianType SegalSugawara Vector Natasha Rozhkovskaya Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66502, U.S.A. rozhkovs@math.ksu.edu [Abstractpdf] \def\o{{\frak o}} A combinatorial formula for the Pfaffian of the universal enveloping algebra $U(\widehat{\o}_{2n})$ of the affine KacMoody algebra $\widehat{\o}_{2n}$ is proved. It allows us easily to compute the image of the SegalSugawara vector under the HarishChandra 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, FeiginFrenkel center, HarishChandra homomorphism. MSC: 17B35, 17B67 [ Fulltextpdf (348 KB)] for subscribers only. 