Casimir elements for certain polynomial current Lie algebras

Research Report MRR96-052

Casimir elements for certain polynomial current Lie algebras

Alexander Molev

Abstract: We consider the polynomial current Lie algebra $\gl(n)[x]$ corresponding to the general linear Lie algebra $\gl(n)$, and its factor-algebra $\g_m$ by the ideal $\sum_{k\geq m}\gl(n)x^k$. We construct two families of algebraically independent generators of the center of the universal enveloping algebra $\U(\g_m)$ by using the quantum determinant and the quantum contraction for the Yangian of level $m$.

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