منابع مشابه
Total Positivity for Loop Groups Ii: Chevalley Generators
This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop the formalism of infinite sequences of braid moves, called a braid limit. We relate this to a partial order, called the limit weak order, on ...
متن کاملSmall degree representations of finite Chevalley groups in defining characteristic
We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l3 and for rank 11 m...
متن کاملGeometric Characterizations of Finite Chevalley Groups of Type B2
Finite Moufang generalized quadrangles were classified in 1974 as a corollary to the classification of finite groups with a split BN-pair of rank 2, by P. Fong and G. M. Seitz (1973), (1974). Later on, work of S. E. Payne and J. A. Thas culminated in an almost complete, elementary proof of that classification; see Finite Generalized Quadrangles, 1984. Using slightly more group theory, first W. ...
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We describe combinatorial techniques to determine the numbers of semisim-ple conjugacy classes and adjoint orbits with xed class of centralizers for simply connected nite groups of Lie type.
متن کاملChevalley groups, reflections groups, braid groups
Program Monday 08h30-09h30 G. Lusztig: On the cleanness of cuspidal character sheaves. 09h45-10h45 P. Achar: Derived Satake equivalence and geometric restriction to a Levi subgroup. 11h15-12h15 G. Williamson: Generators and relations for Soergel bimodules. Tuesday 08h30-09h30 O. Brunat: On semisimple classes in finite reductive groups. 09h45-10h45 R. Charney: Groups Associated to Random Graphs....
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-03073-8