Robert Steinberg wins the Steele Prize

Robert Steinberg was awarded the 1985 Fundamental Paper Steele Prize by the American Mathematical Society at its summer meeting in Laramie, Wyoming. The information below is from Notices of the American Mathematical Society 32 (5) (1985), 575-579.

1985 Fundamental Paper Steele Prize.

The 1985 award for a paper, whether recent or not, which has proved to be of fundamental or lasting importance in its field, or a model of important research, is made to Robert Steinberg for the following series of papers on various aspects of the theory of algebraic groups:

Representations of algebraic groups, Nagoya Mathematical Journal 22 (1963), 33-56.

Regular elements of semisimple algebraic groups, Institut des Hautes Etudes Scientifiques. Publications Mathématiques 25 (1965), 49-80.

Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society 80 (1968), 1-108.

The results and methods contained in these papers have contributed to progress on a wide range of deep and important problems in the theory of finite simple groups, representation theory, and cohomology, as well as in the theory of algebraic groups. This work has helped open the way to the establishment of the theory of algebraic groups as a strong and versatile method for the solution of problems, many of which had long appeared inaccessible.

Response

I want to thank the Steele Prize committee for this award. The news, when I first learned about it, came as a total surprise. To have my name added to the list of distinguished mathematicians who have received this award is indeed an honour. I view the award as a tribute, not just to me, but to all of the people, before and after, who have worked in this field and continue to make it such a vital area of mathematics. Those that preceded me made my own work possible and those that followed are responsible for any lasting value that it may have. It is not possible to name all of the people involved, but I would like to mention two of them, Professors Claude Chevalley and Richard Brauer, both unfortunately now dead. They were primarily responsible for the renewed interest and great surges in the theory of algebraic groups and the theory of finite groups just before the papers cited in the award were written. Brauer was also my main teacher and my indebtedness to him can not be measured. It pleases me a great deal that the first of the three papers chosen by the committee is dedicated to Brauer and has as its takeoff a theorem of his. The main result of that paper is a "tensor product theorem" that simplifies the representation theory of the finite and the algebraic simple groups. The second paper contains the construction of a cross section of the set of regular elements of a semisimple algebraic group similar to the Jordan normal form for matrices and, as a consequence, the theorem that the Galois cohomology of connected algebraic groups defined over fields of dimension at most 1 is trivial. The latter result has been used in the study of groups over local fields and vector bundles over Riemann surfaces. The third paper introduces the notion of affine root system, but one of its main purposes is the development of a connection between the simple algebraic groups and the simple finite groups. The point is that, with some exceptions, each of the latter is the set of fixed points of a suitable endomorphism of one of the former. The first paper and a companion paper on central extensions of algebraic groups were written while I was a visitor at the Institute for Advanced Study in 1961-1962, while the second paper and a preliminary version of the third were written in Paris in 1963-1964. Thus, leaves away from home and the resulting contacts with other mathematicians have been of great benefit to me. Since a number of talented younger mathematicians are now working in the area in which my papers were written, I expect it to remain an active one.

Biographical Sketch

Robert Steinberg was born 25 May 1922, in Stykon, Romania. His undergraduate and graduate studies were done at the University of Toronto, where he received a B.A. in 1944 and a Ph.D. in mathematics in 1948 and was a lecturer in mathematics in 1947-1948. Since 1948 he has been a member of the department of mathematics at the University of California, Los Angeles, as an instructor, assistant professor, associate professor, and (since 1962) a full professor. He has visited the Institute for Advanced Study (1955-1956, 1961-1962, 1969), Yale University (1967-1968), M.I.T. (1968-1969), Tata Institute (1972), and (informally) the University of Paris (1963-1964, 1973) and Queen Mary College (1979-1980). This year he was elected to the National Academy of Sciences.

He has given invited addresses at the AMS meeting in Las Cruces, New Mexico (April 1963), at the International Congress of Mathematicians in Moscow (August 1966), and at the Annual Meeting of the MAA in Las Vegas, Nevada, January 1972. The ICM lecture, Classes of elements of semisimple algebraic groups was published in the Proceedings of the International Congress of Mathematicians (Moscow, 1966), pages 277-284.

He is a member of the American Mathematical Society and the Mathematical Association of America.

Last Updated October 2026