Positive level, negative level and level zero
arXiv:1907.11796
Abstract
This is a survey on the combinatorics and geometry of integrable representations of quantum affine Lie algebras with a particular focus on level 0. Pictures and examples are included to illustrate the affine Weyl group orbits, crystal graphs and Macdonald polynomials that provide detailed understanding of the structure of the extremal weight modules and their characters. The final section surveys the alcove walk method of working with the positive level, negative level and level zero affine flag varieties and describes the corresponding actions of the affine Hecke algebra.
References in corpus (7)
- Quantum Affine Algebras and their Representations
- BGG reciprocity for current algebras
- On Level Zero Representations of Quantized Affine Algebras
- Extremal weight modules of quantum affine algebras
- Demazure submodules of level-zero extremal weight modules and specializations of Macdonald polynomials
- Weyl Modules for Classical and Quantum Affine algebras
- Semi-infinite Lakshmibai-Seshadri path model for level-zero extremal weight modules over quantum affine algebras