Verma-Type Modules for Quantum Affine Lie Algebras
by Futorny, Vyacheslav M.; Grishkov, Alexander N.; Melville, Duncan J.
Let
$\mathfrak{g}$
be an untwisted affine Kac–Moody algebra and MJ(λ) a Verma-type module for
$\mathfrak{g}$
with J-highest weight λ∈P. We construct quantum Verma-type modules MJq(λ) over the quantum group
$U_{q}(\mathfrak{g})$
, investigate their properties and show that MJq(λ) is a true quantum deformation of MJ(λ) in the sense that the weight structure is preserved under the deformation. We also analyze the submodule structure of quantum Verma-type modules.
DOI: 10.1007/s10468-004-5765-z
Print publication date: 3/1/2005
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