RETROSPECTIVE RETROSPECTIVE Robert Steinberg, 1922–2014 V. S. Varadarajan1 Department of Mathematics, University of California, Los Angeles, CA 90095-1555 I have had a good life a distinguished career, and the citation singled (Ik heb een goed leven gehad) out several of his great papers. All of his papers can be found in Robert Steinberg, This quotation (in English and Dutch) was Collected Papers, AMS, 1997. exactly how Tonny Springer, a famous math- He was awarded the Jeffery–Williams prize ematician from Utrecht in Holland and one of the Canadian Mathematical Society in of Robert Steinberg’s closest friends both per- 1990. He was an invited speaker at the sonally and mathematically, wanted his life International Congress of Mathematicians described after his death. It is also a perfect in Moscow in 1966. In 2003, the Journal of description of Robert Steinberg’slife. Algebra published a special issue to celebrate Bob was born on 25 May 1922, in Soroki, his 80th birthday. Bessarabia, Romania (present day Soroca, He must be regarded as one of the great Moldova) and came to settle in Canada with mathematicians of our time. His main in- his parents when he was still very young. He terest was in the theory of algebraic groups, was a student of Richard Brauer in Toronto, especially semisimple groups, and his discov- receiving his PhD in 1948, and he joined eriesinthisarearankhimamongthe University of California, Los Angeles (UCLA) ’ in 1948, where he stayed until the end. He had subject s greatest innovators with the likes 12 PhD students complete their dissertations of Armand Borel and Claude Chevalley. His Robert Steinberg. Image courtesy of David with him. He married Maria Alice née Weber results were profound and yet his methods Weisbart. in 1952 and settled down in Pacific Palisades, were ultimately simple and transparent, a asmallsuburbancommunityofLosAngeles characteristic that only a truly great master can achieve. notes in mathematics that I can think of. near the Pacific Ocean. They led a simple life, The theory of groups and algebras is littered and their house was always open for countless He discovered new finite simple groups, going beyond what Chevalley had done. He with concepts and ideas originating from mathematicians and friends. I myself joined him: Steinberg cocycles, Steinberg symbols, UCLA in 1965, and my wife Veda and I be- constructed the universal Chevalley group, the Steinberg character, Steinberg triples, came very good friends of theirs, especially showed it is a universal central extension of Steinberg groups, and so on, to mention because of the closeness of my mathematical all Chevalley groups, and discovered the just a few. interests with his and the proximity of our essential relations (Steinberg symbols) in the When Maria passed away last year, it was homes. We were fortunate to go to the center of this group. His results are heavily a cruel blow to Bob. In the last few months lunches Maria arranged on Easter Sundays. used in algebraic K-theory and the construc- after she passed away, I drew closer to him Bob and Maria were avid hikers and liked to tion of covering groups of algebraic groups and visited him once every two weeks or go camping in the Yosemite and Sequouia over local fields and adeles. He solved so, discussing many things. I like to believe National Parks, which they did almost annu- a famous conjecture of Serre by constructing that these visits were pleasant and enjoy- ally. His was a gentle personality, full of hu- an affine section of the orbits of maximal able to him. mor and good sense, and he and Maria were dimension of a simply connected semi simple It was a great good fortune for me to have an inseparable unit, almost like two quarks. group. He discovered what is now called the been a friend of his for almost 50 years and to They made generous gifts to the American Steinberg representation, which occurs all admire up close his greatness that was Mathematical Society (AMS) and were mem- over the place in representation theory and intertwined with simplicity and modesty. I bers of the President’sAssociatesoftheAMS. automorphic forms. In all, his impact on the will miss him very much, as will all He was elected to the National Academy of theory of algebraic groups and finite groups his friends. Sciences in 1985. His comment to me in has been monumental. a letter he wrote to me on that occasion was His famous lecture notes on Chevalley that it proved he still had friends in the groups, written while he lectured on that A version of this Retrospective was previously published in the Academy; the letter contained more about topic in Yale, in 1967, are a masterpiece of UCLA Department of Mathematics Newsletter. theLakersandCelticsthanhishonor!He brevity, comprehensiveness, and beauty. They Author contributions: V.S.V. wrote the paper. won the Leroy Steele prize of the AMS for are probably the most famous unpublished 1Email: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1419483111 PNAS | December 16, 2014 | vol. 111 | no. 50 | 17689 Downloaded by guest on September 29, 2021.