Journal of Lie Theory

no. 2
A New Formula for the Pfaffian-Type Segal-Sugawara Vector
Journal of Lie Theory, Volume 24 (2014) no. 2, pp. 529-543
\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.
DOI: 10.5802/jolt.795
Classification: 17B35, 17B67
Keywords: Pfaffian, affine orthogonal Lie algebra, Feigin-Frenkel center, Harish-Chandra homomorphism 
@article{JOLT_2014_24_2_a10,
     author = {N. Rozhkovskaya},
     title = {A {New}  {Formula} for the  {Pfaffian-Type} {Segal-Sugawara}  {Vector}},
     journal = {Journal of Lie Theory},
     pages = {529--543},
     year = {2014},
     volume = {24},
     number = {2},
     doi = {10.5802/jolt.795},
     zbl = {1321.17009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.795/}
}
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N. Rozhkovskaya. A New  Formula for the  Pfaffian-Type Segal-Sugawara  Vector. Journal of Lie Theory, Volume 24 (2014) no. 2, pp. 529-543. doi: 10.5802/jolt.795

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