Classification of irreducible weight modules over $W$-algebra W(2,2)

Abstract

We show that the support of an irreducible weight module over the $W$-algebra $W(2,2)$, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the the $W$-algebra $W(2,2)$, having a nontrivial finite dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module of the intermediate series).

10 pages

References in corpus (3)

• Classification of Harish-Chandra Modules over the Higher Rank Virasoro Algebras
• Harish-Chandra Modules Over the Twisted Heisenberg-Virasoro Algebra
• Classification of Harish-Chandra modules over the $W$-algebra W(2,2)

Cited by in corpus (13)

• Modules over the Heisenberg-Virasoro and $W(2,2)$ algebras
• Classification of Harish-Chandra modules over the $W$-algebra W(2,2)
• Whittaker Modules For The W-algebra W(2,2)
• Galilean conformal algebras in two spatial dimension
• Lie bialgebra structures on the $W$-algebra W(2,2)
• Higher-order Galilean contractions
• q-Deformation of W(2,2) Lie algebra associated with quantum groups
• $k$-Modules over linear spaces by $n$-linear maps admitting a multiplicative basis
• Weight modules over split Lie algebras
• Quantum group structure of the q-deformed $W$ algebra $\WW_q$
• Whittaker modules for a Lie algebra of Block type
• Whittaker Modules for Graded Lie Algebras
• Weight modules for map (super)algebra related to the Virasoro algebra