Prasad Senesi
Irreducible finite-dimensional representations of equivariant map algebras.
Fri, 09/18/2009 - 11:36 — SomNambulAuthors: Prasad Senesi, Erhard Neher, Alistair Savage
Subjects: Representation Theory
AbstractSuppose a finite group acts on a scheme X and a finite-dimensional Lie
algebra g. The corresponding equivariant map algebra is the Lie algebra M of
equivariant regular maps from X to g. We classify the irreducible
finite-dimensional representations of these algebras. In particular, we show
that all such representations are tensor products of evaluation representations
and one-dimensional representations, and we establish conditions ensuring that
they are all evaluation representations. For example, this is always the case
if M is perfect.Irreducible finite-dimensional representations of equivariant map algebras.
Fri, 09/18/2009 - 11:36 — SomNambulAuthors: Prasad Senesi, Erhard Neher, Alistair Savage
Subjects: Representation Theory
AbstractSuppose a finite group acts on a scheme X and a finite-dimensional Lie
algebra g. The corresponding equivariant map algebra is the Lie algebra M of
equivariant regular maps from X to g. We classify the irreducible
finite-dimensional representations of these algebras. In particular, we show
that all such representations are tensor products of evaluation representations
and one-dimensional representations, and we establish conditions ensuring that
they are all evaluation representations. For example, this is always the case
if M is perfect.A block decomposition of finite-dimensional representations of twisted loop algebras.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Prasad Senesi
Subjects: Representation Theory
AbstractIn this paper we consider the category of F^\sigma of finite-dimensional
representations of a twisted loop algebra corresponding to a finite-dimensional
Lie algebra with non-trivial diagram automorphism. Although F^\sigma is not
semisimple, it can be written as a sum of indecomposable subcategories (the
blocks of the category). To describe these summands, we introduce the twisted
spectral characters for the twisted loop algebra.Finite-dimensional representation theory of loop algebras: a survey.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Prasad Senesi
Subjects: Representation Theory
AbstractWe survey some important results concerning the finite--dimensional
representations of the loop algebra of a simple complex Lie algebra, and their
twisted loop subalgebras. In particular, we review the parametrization and
description of the Weyl modules and of the irreducible finite--dimensional
representations of such algebras, describe a block decomposition of the
(non--semisimple) category of their finite--dimensional representations, and
conclude with recent developments in the representation theory of multiloop
algebras.
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