Kazhdan, David; Lusztig, George Affine Lie algebras and quantum groups. (English) Zbl 0726.17015 Int. Math. Res. Not. 1991, No. 2, 21-29 (1991). 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. Reviewer: D.Leites (Stockholm) Cited in 2 ReviewsCited in 45 Documents 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 Keywords:quantum groups; representations; simply laced affine Kac-Moody algebra; tensor category; intersection cohomology of infinite-dimensional Schubert varieties; Knizhnik-Zamolodchikov equations PDFBibTeX XMLCite \textit{D. Kazhdan} and \textit{G. Lusztig}, Int. Math. Res. Not. 1991, No. 2, 21--29 (1991; Zbl 0726.17015) Full Text: DOI