学术报告（Alexander Molev 11.9）

摘要：

The canonical symmetrization map is a g-module isomorphism between the symmetric algebra S(g) of a finite-dimensional Lie algebra g and its universal enveloping algebra U(g). This implies that the images of g-invariants in S(g) are Casimir elements. For each simple Lie algebra g of classical type, we consider basic ginvariants arising from the characteristic polynomial of the matrix of generators. We calculate the Harish-Chandraimages of the corresponding Casimir elements. By using counterparts of the symmetric algebra invariants for the associated affine Kac-Moody algebras we obtain new formulas for generators of the centers of the affine vertex algebras at the critical level.