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10 papers · 1 filter
Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus
Yuly Billig, Alexander Molev, Ruibin Zhang
We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choic…
Representations of Truncated Current Lie Algebras
Benjamin J. Wilson
Let g denote a Lie algebra, and let T(g) denote the tensor product of g with a ring of truncated polynomials. The Lie algebra T(g) is called a truncated current Lie algebra. The hi…
Highest-Weight Theory for Truncated Current Lie Algebras
Benjamin J. Wilson
Let g denote a Lie algebra over a field of characteristic zero, and let T(g) denote the tensor product of g with a ring of truncated polynomials. The Lie algebra T(g) is called a t…
On the lowest two-sided cell in affine Weyl groups
Jeremie Guilhot
Bremke and Xi determined the lowest two-sided cell for affine Weyl groups with unequal parameters and showed that it consists of at most |W_{0}| left cells where W_{0} is the assoc…
Imaginary highest-weight representation theory and symmetric functions
Benjamin J. Wilson
Affine Lie algebras admit non-classical highest-weight theories through alternative partitions of the root system. Although significant inroads have been made, much of the classica…
Homomorphisms and Higher Extensions for Schur algebras and symmetric groups
Anton Cox, Alison Parker
This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. W…