Robert Steinberg ^People

He introduced the Steinberg representation, the Lang-Steinberg theorem, the Steinberg group in algebraic K-theory, Steinberg's formula in representation theory, and the Steinberg groups in Lie theory that yield finite simple groups over finite fields.He discovered new finite simple groups, going beyond what Chevalley had done. He constructed the universal Chevalley group, showed ti is a univer- sal central extension of al Chevalley groups, and discovered the essential relations (Steinberg symbols) in the center ofthis group. His results are heavily used in algebraicK-theory and the construction of covering groups of algebraic groups over local fields and adeles. He solved a famous conjectureof Serre by constructing an affine section ofthe orbits of maximal dimension of a simply connected semi simple group. He disco- vered what is now called the Steinberg representation, which occurs all over the place in representation theory and automorphic forms. In all, his impact on the theory of algebraic groups and finite groups has been monumental. His famous lecture notes on Chevalley groups, written while he lectured on that topic in Yale, in 1967, are a masterpiece of brevity, comprehensiveness, and beauty. They are probably the most fa- mous unpublished notes in mathematics that I can think of. The theory of groups and algebras is littered with concepts and ideas originating from him: Steinberg cocycles, Steinberg symbols, the Steinberg character, Steinberg triples, Steinberg groups.