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Description: |
Usually in representation theory one studies homomorphisms of a complicated group G into a simpler group: the general linear group of a vector space. But it is also interesting to replace the general linear group by other algebraic groups such as
symplectic, orthogonal or even exceptional groups. To begin with one should consider the case where G is the alternating group in 5 letters, the smallest nonabelian simple group. This case is already non-trivial. We will discuss recent progress on this problem.
George Lusztig was born in Timisoara, Romania, 20 May 1946. He obtained the
Licenta in Matematica, Bucharest Univ. (1968), and PhD at Princeton Univ. (1971).
Since 1999 he is Norbert Wiener professor in Massachusetts Institute of Technology, USA. Author of 174 papers (already in print), he has participated and been in the scientific committees of most international conferences on quantum group and representation theory. He is fellow of the Royal Society (of London) and member of U.S.National Academy of Sciences.
George Lusztig has received the 1999 gold Brouwer Medal of the Dutch
Mathematical Society. Wilberd van der Kallen, chair of the selection committee
for the 1999 Brouwer Medal, presented the laudatio for the prize. The laudatio says that the prize was given for Lusztig's "many deep and influential contributions to representation theory." In particular, the following three
achievements were cited:
1. The construction with Deligne of what are now called Deligne-Lusztig characters (Ann. of Math., 1976) and Lusztig's ensuing project to classify all the characters of finite reductive groups (cf. Lusztig's 1984 book).
2. The invention with Kazhdan (Invent. Math., 1979) of what are now called Kazhdan-Lusztig polynomials and the many conjectures and theorems that link them to different parts of representation theory.
3. The construction of quantum groups over the integers and the construction of canonical bases (for classical representations of simple complex Lie groups) and their
positivity properties (cf. Lusztig's 1993 book). Lusztig's recent work on totally positive matrices belongs in this context.
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| Start Date: |
2006-06-27 |
| Start Time: |
15:00 |
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Speaker: |
George Lusztig (Dept. Math., MIT)
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Place: |
Sala 2.4 - Departamento de Matemática
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See more:
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