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Explicit formulas for Segal–Sugawara vectors associated with the simple Lie algebra g of type G2 are found by using computer-assisted calculations. This leads to a direct proof of the Feigin–Frenkel theorem describing the center of the corresponding affine vertex algebra at the critical level. As an application, we give an explicit solution of Vinberg's quantization problem by providing formulas for...
We consider Casimir elements for the orthogonal and symplectic Lie algebras constructed with the use of the Brauer algebra. We calculate the images of these elements under the Harish-Chandra isomorphism and thus show that they (together with the Pfaffian-type element in the even orthogonal case) are algebraically independent generators of the centers of the corresponding universal enveloping algebras.
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