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New irreducible modules for affine Lie algebras at the critical level
 

Summary: New irreducible modules for affine Lie algebras
at the critical level
DraŸzen Adamovi'c
Let g be a simple finite­dimensional Lie algebra and “ g the associated affine
Lie algebra. Let V (¯) be a loop module for “ g corresponding to irreducible
finite­dimensional g--module V (¯) and let L(–) be an irreducible highest
weight module (see Section 1). Then the tensor product V
(¯)\Omega L(–) has
infinite­dimensional weight spaces. In the case of integrable modules such
modules were studied by V. Chari and A. Pressley ([CP]). They proved that
the “
g--module V
(¯)\Omega L(–) is irreducible if the weight ¯ is ''large'' compared
with – (see [CP, Theorem 2.2]). Their construction gave the first examples
of such irreducible “
g--modules.
One of the motivations for study these modules are intertwining operators
between certain modules over affine Lie algebras at the fixed level ` , i.e. “
g--
morphisms

  

Source: Adamovic, Drazen - Department of Mathematics, University of Zagreb

 

Collections: Mathematics