 
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 gmodule 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 “
gmodule 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 “
gmodules.
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
