10 citations · 14 across the 6 of their papers we have counts for
6 papers
A Weyl Module Stratification of Integrable Representations (with an appendix by Ryosuke Kodera)
Syu Kato, Sergey Loktev
We construct a filtration on integrable highest weight module of an affine Lie algebra whose adjoint graded quotient is a direct sum of global Weyl modules. We show that the graded…
Macdonald Polynomials and BGG reciprocity for current algebras
Matthew Bennett, Arkady Berenstein, Vyjayanthi Chari +2
We study the category of graded representations with finite--dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similariti…
An application of global Weyl modules of $\lie{sl}_{n+1}[t]$ to invariant theory
Vyjayanthi Chari, Sergey Loktev
We identify $\lie{sl}_{n+1}$--isotypical components of global Weyl modules with natural subspaces in a polynomial ring, and then apply the representation theory of current algebras…
Klein Topological Field Theories from Group Representations
Sergey A. Loktev, Sergey M. Natanzon
We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We…
Double affine Lie algebras and finite groups
Nicolas Guay, David Hernandez, Sergey Loktev
We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on t…
A Lie-theoretic construction of spherical symplectic reflection algebras
P. Etingof, S. Loktev, A. Oblomkov +1
We propose a construction of the spherical subalgebra of a symplectic reflection algebra of an arbitrary rank corresponding to a star-shaped affine Dynkin diagram. Namely, it is ob…