Irreducible A⁽¹⁾₁ -modules from modules over two-dimensional non-abelian Lie algebra

Abstract

For any module V over the two-dimensional non-abelian Lie algebra b and scalar α∈ℂ, we define a class of weight modules F^α(V) with zero central charge over the affine Lie algebra A⁽¹⁾₁. These weight modules have infinitedimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules F^α(V) to be irreducible. In this way, we obtain a lot of irreducible weight A⁽¹⁾₁-modules with infinite-dimensional weight spaces.

Key words： Affine Lie algebras; irreducible modules; weight modules

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