Related Research Articles
Bertram Kostant was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.
Alexandre Aleksandrovich Kirilloff is a Soviet and Russian mathematician, known for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory. He is an emeritus professor at the University of Pennsylvania.
In mathematics, the orbit method establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits: orbits of the action of the group on the dual space of its Lie algebra. The theory was introduced by Kirillov for nilpotent groups and later extended by Bertram Kostant, Louis Auslander, Lajos Pukánszky and others to the case of solvable groups. Roger Howe found a version of the orbit method that applies to p-adic Lie groups. David Vogan proposed that the orbit method should serve as a unifying principle in the description of the unitary duals of real reductive Lie groups.
Victor Gershevich (Grigorievich) Kac is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.
The Atlas of Lie Groups and Representations is a mathematical project to solve the problem of the unitary dual for real reductive Lie groups.
David Alexander Vogan Jr. is a mathematician at the Massachusetts Institute of Technology who works on unitary representations of simple Lie groups.
In mathematics, a Zuckerman functor is used to construct representations of real reductive Lie groups from representations of Levi subgroups. They were introduced by Gregg Zuckerman (1978). The Bernstein functor is closely related.
Gregg Jay Zuckerman 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.
In mathematics, the Langlands classification is a description of the irreducible representations of a reductive Lie group G, suggested by Robert Langlands (1973). There are two slightly different versions of the Langlands classification. One of these describes the irreducible admissible (g, K)-modules, for g a Lie algebra of a reductive Lie group G, with maximal compact subgroup K, in terms of tempered representations of smaller groups. The tempered representations were in turn classified by Anthony Knapp and Gregg Zuckerman. The other version of the Langlands classification divides the irreducible representations into L-packets, and classifies the L-packets in terms of certain homomorphisms of the Weil group of R or C into the Langlands dual group.
Anthony William Knapp is an American mathematician and professor emeritus at the State University of New York, Stony Brook working in representation theory. For much of his career, Knapp was a professor at Cornell University.
Jeffrey David Adams (born 1956) is a mathematician at the University of Maryland who works on unitary representations of reductive Lie groups and who led the project Atlas of Lie Groups and Representations that calculated the characters of the representations of E8. The project to calculate the representations of E8 has been compared to the Human Genome Project in scope. Together with Dan Barbasch and David Vogan, he co-authored a monograph on a geometric approach to the Langlands classification and Arthur's conjectures in the real case.
In mathematics, specifically in the representation theory of Lie groups, a Harish-Chandra module, named after the Indian mathematician and physicist Harish-Chandra, is a representation of a real Lie group, associated to a general representation, with regularity and finiteness conditions. When the associated representation is a -module, then its Harish-Chandra module is a representation with desirable factorization properties.
Jens Carsten Jantzen is a German mathematician and professor emeritus at Aarhus University working on representation theory and algebraic groups. He introduced the Jantzen filtration and translation functors.
In mathematical representation theory, a translation functor is a functor taking representations of a Lie algebra to representations with a possibly different central character. Translation functors were introduced independently by Zuckerman and Jantzen. Roughly speaking, the functor is given by taking a tensor product with a finite-dimensional representation, and then taking a subspace with some central character.
In mathematics, a unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups.
In the field of mathematics known as representation theory, an L-packet is a collection of irreducible representations of a reductive group over a local field, that are L-indistinguishable, meaning they have the same Langlands parameter, and so have the same L-function and ε-factors. L-packets were introduced by Robert Langlands in, .
In mathematical representation theory, the Eisenstein integral is an integral introduced by Harish-Chandra in the representation theory of semisimple Lie groups, analogous to Eisenstein series in the theory of automorphic forms. Harish-Chandra used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgroups. Trombi gave a survey of Harish-Chandra's work on this.
Nolan Russell Wallach is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the two-volume treatise Real Reductive Groups.
Jing-Song Huang is a Chair Professor in the Department of Mathematics of Hong Kong University of Science and Technology. His research interests are representations of Lie groups and harmonic analysis. After graduating from Peking University, he went to Massachusetts Institute of Technology and received his PhD degree in 1989, under the supervision of David Vogan.
Kari Kaleva Vilonen is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.
References
- 1 2 3 "Peter Trapa selected as new dean of the College of Science | UNews". unews.utah.edu. Retrieved 11 May 2021.
- ↑ "Atlas of Lie Groups and Representations". www.liegroups.org. Retrieved 11 May 2021.
- ↑ "Peter E. Trapa - Bio". www.math.utah.edu. Retrieved 11 May 2021.
- ↑ "Web page for David Vogan". www-math.mit.edu. Retrieved 11 May 2021.
- ↑ "Atlas of Lie Groups and Representations". www.liegroups.org. Retrieved 11 May 2021.
- ↑ "Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 11 May 2021.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
