New Directions in Representation Theory
Identifieur interne : 001609 ( Istex/Curation ); précédent : 001608; suivant : 001610New Directions in Representation Theory
Auteurs : Charles W. Curtis [États-Unis]Source :
- Milan Journal of Mathematics [ 1424-9286 ] ; 2012-06-01.
Abstract
Abstract: The Iwahori–Hecke algebra H(G, B) of a finite Chevalley group G with respect to a Borel subgroup B is described as a deformation of the group algebra of the Weyl group of G Similarly, the +-part of the quantized enveloping algebra $${{U^+_v (\mathfrak{g})}}$$ associated with a semisimple Lie algebra $${{\mathfrak{g}}}$$ can be viewed as a deformation of the +-part of the universal enveloping algebra $${{U(\mathfrak{g})}}$$ . In both cases it is shown how information concerning the deformed algebras H(G, B) and $${{U^+_v (\mathfrak{g})}}$$ can be used to obtain results about the representation theory of the Chevalley group G and the semisimple Lie algebra $${{\mathfrak{g}}}$$ .
Url:
DOI: 10.1007/s00032-012-0177-8
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