Representations of the Extended W-Algebra

Abstract

In this article, classification of all irreducible Harish–Chandra modules over (the universal central extension of W(α, β)) for a i = 0, b i ≠ 1, i = 1, 2 is given. In addition, classification of irreducible weight modules with a finite dimensional weight space over for a i = 0, − 1 ≤ b i ≠ 1 if b i ∈ ℤ, i = 1, 2 is also obtained. Finally, we study the irreducibility of Verma modules over a subalgebra of .