On Finite W-Algebras for Lie Superalgebras in Non-Regular Case

On the finite W-algebra for the Lie superalgebra Q(N) in the non-regular case

“…In this work we consider the case when the corresponding nilpotent element has Jordan blocks each of size l. We construct a set of generators of W χ (Theorem 5.1) and prove that W χ is isomorphic to a quotient of the super-Yangian of Q( n l ) (Theorem 4.2 and Corollary 5.9). This proves the conjecture, which we formulated in [14].…”

“…The general definition of a finite W -algebra was given by A. Premet in [15] (see also [7]). In the case of Lie superalgebras, finite W -algebras have been extensively studied by mathematicians and physicists in [1,2,[10][11][12][13][14][18][19][20].…”