George Lusztig

George Lusztig, actually Gheorghe Lusztig, ( born 1946 in Timişoara, Romania) is an American mathematician who deals with representation theory.

Lusztig studied at the University of Bucharest. Then he went to the USA where he from 1969 to 1971 at the Institute for Advanced Study in Princeton worked with Michael Atiyah. In 1971 he received his doctorate at Princeton in Atiyah and (formal) William Browder ( Novikov 's Higher Signature and Families of Elliptic Operators, published in the Journal of Differential Geometry Bd.7, 1972, p.229 ). From 1971 he was at the University of Warwick in England, where in 1972 he was Lecturer and Professor in 1974. From 1978 he worked at the Massachusetts Institute of Technology (MIT ), where he is currently Professor Norbert Wiener.

Lusztig introduced new fundamental concepts in the representation theory of algebraic groups. In the Deligne - Lusztig theory ( with Pierre Deligne, Representations of reductive groups over finite fields, Annals of Mathematics, Vol 103, 1976, p.103 -161 ) is used, the -adic cohomology to linear representations of finite groups of Lie - type to construct. In 1984, Lusztig on so all representations of finite simple groups of Lie type. In the work Representation of Coxeter groups and Hecke algebras ( Inventiones Mathematicae Bd.53, 1979, p.165 ) Kazhdan and Lusztig 1979 Kazhdan - Lusztig polynomials introduced ( and formulated the Kazhdan - Lusztig conjectures ) and gave an interpretation in 1980 with the Schnittkohomologie of Goresky and Robert MacPherson. Lusztig wore on the application of " geometric " methods in representation theory at the International Congress of Mathematicians in 1990 in Kyoto before ( Intersection Cohomology Methods in Representation Theory ). From the late 1980s, he was also with quantum groups (defined in 1985 by Vladimir Drinfeld and Michio Jimbo ).

In 1977 he was awarded the Junior Berwick Prize of the London Mathematical Society. In 1985 he received the Cole prize in algebra. Since 1992 he is a member of the National Academy of Sciences. In 2008 he received the Leroy P. Steele Prize and 1999, the Brouwer Medal. In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver ( On the discrete series representations of the classical groups over finite fields ), as well as in 1990 in Kyoto ( Intersection cohomology methods in representation theory ) and in 1983 in Warsaw ( Characters of reductive groups over finite fields ).

His doctoral counted Ian Grojnowski (1992) and Corrado de Concini.

Writings

• The Discrete Series of over a Finite Field. Annals of Mathematical Studies, Princeton 1974.
• Characters of Reductive Groups over a Finite Field. Annals of Mathematical Studies, Princeton 1984.
• Introduction to Quantum Groups. In 1993.