Abstract
We discuss finite-dimensional representations of current algebras, that is, Lie algebras of polynomials in several variables with values in a reductive Lie algebra. Weyl modules are universal among finite-dimensional repsesentations, generated by a common eigenvector with respect to the action of currents with values in a Borel subalgebra.
We relate the space of diagonal harmonics and its generalizations to these modules and discuss the underlying combinatorics, involving a wide generalization of Catalan and Narayana numbers.
Related Links
- http://arxiv.org/abs/0806.0170 - arXiv preprint
- http://arxiv.org/abs/0901.3205 - arXiv preprint
- http://arxiv.org/abs/math/0503315 - arXiv preprint
- http://arxiv.org/abs/math/0502165 - arXiv preprint
- http://arxiv.org/abs/math/0312158 - arXiv preprint
- http://arxiv.org/abs/math/0212001 - arXiv preprint