Abstract
The theory of quantum groups originates in completely integrable models of statistical mechanics and quantum field theory (see [FRT], [J4]). It becomes a truly mathematical theory with the independent discovery by Drinfeld [Dl] and Jimbo [J1] of a q-deformation of the universal enveloping algebra of an arbitrary Kac-Moody algebra. This remarkable result immediately raised numerous questions about q-deformations of various structures associated to Kac-Moody algebras. A major step in this direction was done by Lusztig [L], who obtained a q-deformation of the category of highest weight representations of Kac-Moody algebras for generic or formal parameter q.
Dedicated to Bertram Kostant
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Ding, J., Frenkel, I.B. (1994). Spinor and Oscillator Representations of Quantum Groups. In: Brylinski, JL., Brylinski, R., Guillemin, V., Kac, V. (eds) Lie Theory and Geometry. Progress in Mathematics, vol 123. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0261-5_5
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