Elementary invariants for centralizers of nilpotent matrices

Abstract

We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the Lie algebra gl_N(C). In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova (math.RT/0610049).

12 pages

References in corpus (1)

• Parabolic presentations of the Yangian Y(gl_n)

Cited by in corpus (7)

• A quantum Mirković-Vybornov isomorphism
• Invariants of the vacuum module associated with the Lie superalgebra gl(1|1)
• Center at the critical level for centralizers in type $A$
• Casimir elements and Sugawara operators for Takiff algebras
• Classical $\mathcal{W}$-algebras for centralizers
• $W$-algebras associated with centralizers in type $A$
• Generalized finite and affine $W$-algebras in type $A$