Classical $\mathcal{W}$algebras for centralizers
Abstract
We introduce a new family of Poisson vertex algebras $\mathcal{W}(\mathfrak{a})$ analogous to the classical $\mathcal{W}$algebras. The algebra $\mathcal{W}(\mathfrak{a})$ is associated with the centralizer $\mathfrak{a}$ of an arbitrary nilpotent element in $\mathfrak{gl}_N$. We show that $\mathcal{W}(\mathfrak{a})$ is an algebra of polynomials in infinitely many variables and produce its free generators in an explicit form. This implies that $\mathcal{W}(\mathfrak{a})$ is isomorphic to the center at the critical level of the affine vertex algebra associated with $\mathfrak{a}$.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.08645
 Bibcode:
 2019arXiv191108645M
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics
 EPrint:
 15 pages