New irreducible modules for Heisenberg and affine Lie algebras

JOURNAL OF ALGEBRA

卷:373

Article

Bekkert, Viktor²  Benkart, Georgia¹  Futorny, Vyacheslav³  Kashuba, Iryna³ 

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Univ Fed Minas Gerais, ICEx, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

[3] Univ Sao Paulo, Inst Math, BR-05314970 Sao Paulo, Brazil

关键词: Heisenberg Lie algebra;    Affine Lie algebra;    Irreducible module;    Imaginary Verma module;   

DOI  :  10.1016/j.jalgebra.2012.09.035

来源: Elsevier

【 摘 要 】

We study Z-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie algebras. We construct new families of such irreducible modules over Heisenberg Lie algebras. Our main result establishes the irreducibility of the corresponding generalized loop modules providing an explicit construction of many new examples of irreducible modules for affine Lie algebras. In particular, to any function phi : N -> {+/-} we associate phi-highest weight module over the Heisenberg Lie algebra and a phi-imaginary Verma module over the affine Lie algebra. We show that any phi-imaginary Verma module of nonzero level is irreducible. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free