64 research outputs found
Stability of the Chari-Pressley-Loktev bases for local Weyl modules of
We prove stability of the Chari-Pressley-Loktev bases for natural inclusions
of local Weyl modules of the current algebra . These modules being
known to be Demazure submodules in the level 1 representations of the affine
Lie algebra , we obtain, by passage to the direct limit, bases
for the level 1 representations themselves.Comment: 20 pages; minor revision
A survey of equivariant map algebras with open problems
This paper presents an overview of the current state of knowledge in the
field of equivariant map algebras and discusses some open problems in this
area.Comment: 18 pages. v2: Minor correction
New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules
New graded modules for the current algebra of are
introduced. Relating these modules to the fusion product of simple
-modules and local Weyl modules of truncated current algebras
shows their expected impact on several outstanding conjectures. We further
generalize results on PBW filtrations of simple -modules and
use them to provide decomposition formulas for these new modules in important
cases.Comment: 23 page
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