Gregg Jay Zuckerman (born 1949) is a mathematician and professor at Yale University working in representation theory. He discovered Zuckerman functors and translation functors, and with Anthony W. Knapp classified the irreducible tempered representations of semisimple Lie groups.
Education edit
He received his Ph.D. in mathematics from Princeton University in 1975 after completing a doctoral dissertation, titled "Some character identities for semisimple Lie groups", under the supervision of Elias M. Stein.[1]
Research edit
In the late 1970s, Zuckerman and Jens Carsten Jantzen independently introduced translation functors.[2][3] In 1978, he introduced the Zuckerman functor.[2]
In a series of papers from 1976 to 1984, Anthony W. Knapp and Zuckerman gave the classification of tempered representations of semisimple Lie groups.[4][5][6][7]
References edit
- ^ Zuckerman, Gregg (1975). Some character identities for semisimple Lie groups.
- ^ a b Knapp, Anthony W.; Vogan, David A. (1995), Cohomological induction and unitary representations, Princeton Mathematical Series, vol. 45, Princeton University Press, doi:10.1515/9781400883936, ISBN 978-0-691-03756-1, MR 1330919
- ^ Zuckerman, Gregg (1977), "Tensor products of finite and infinite dimensional representations of semisimple Lie groups", Ann. Math., 2, 106 (2): 295–308, doi:10.2307/1971097, JSTOR 1971097, MR 0457636
- ^ Knapp, Anthony W.; Zuckerman, Gregg (1976), "Classification of irreducible tempered representations of semi-simple Lie groups", Proceedings of the National Academy of Sciences of the United States of America, 73 (7): 2178–2180, Bibcode:1976PNAS...73.2178K, doi:10.1073/pnas.73.7.2178, ISSN 0027-8424, JSTOR 65732, MR 0460545, PMC 430485, PMID 16592331
- ^ Knapp, Anthony W.; Zuckerman, Gregg J. (1982), "Classification of irreducible tempered representations of semisimple groups. Part I", Annals of Mathematics, Second Series, 116 (2): 389–455, doi:10.2307/2007066, ISSN 0003-486X, JSTOR 2007066, MR 0672840
- ^ Knapp, Anthony W.; Zuckerman, Gregg J. (1982), "Classification of irreducible tempered representations of semisimple groups. Part II", Annals of Mathematics, Second Series, 116 (3): 457–501, doi:10.2307/2007019, ISSN 0003-486X, JSTOR 2007019, MR 0672840
- ^ Knapp, Anthony W.; Zuckerman, Gregg J. (1984), "Correction", Annals of Mathematics, Second Series, 119 (3): 639, doi:10.2307/2007089, ISSN 0003-486X, JSTOR 2007089, MR 0744867