×

Affine Lie algebras and quantum groups. (English) Zbl 0726.17015

On a category of representations of a simply laced affine Kac-Moody algebra \(\tilde{\mathfrak g}\) (category O, basically) a tensor structure is introduced and the obtained tensor category is equivalent to that of finite-dimensional representations of the quantum algebra corresponding to \({\mathfrak g}\). Via references relations with Gal(\({\bar {\mathbb{Q}}}/{\mathbb{Q}})\), intersection cohomology of infinite-dimensional Schubert varieties and physics, represented by Knizhnik-Zamolodchikov equations, can be detected.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
14M15 Grassmannians, Schubert varieties, flag manifolds
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
PDFBibTeX XMLCite
Full Text: DOI