Alexander Alexandrovich Kirillov
Alexander Alexandrowitsch Kirillow ( Russian Александр Александрович Кириллов , English transliteration Alexandre Aleksandrovich Kirillov ; born May 9, 1936 ) is a Russian mathematician who deals with representation theory of Lie groups and now teaches in the USA .
Kirillow studied at the Lomonosov University in Moscow , where he received his doctorate in 1962 under Israel Gelfand on Unitary representations of nilpotent Lie groups (Russian Mathematical Surveys Vol. 17, 1962, pp. 57-110). Then he was a professor at Lomonosov University. In 1994 he became Francis J. Carey Professor of Mathematics at the University of Pennsylvania .
Kirillov is known for the orbit method in Lie group representation theory. Kirillov originally only investigated nilpotent Lie groups , where he showed that the irreducible unitary representations (except for unitary equivalence) are classified by the "orbit" of the maps of in the dual Lie algebra (coadjoint orbits) of . The orbit method was extended to solvable Lie groups by Bertram Kostant , Louis Auslander , Lajos Pukánszky and others. From his orbit method, he also derived a formula for the characters of the irreducible representations of the Lie group (Kirillov character formula).
Kirillov also sees a version of geometric quantization in his orbit method.
In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Infinite dimensional groups, their representations, orbits, invariants ), 1966 in Moscow ( Theory of the representation of groups , with Mark Graev ) and 1962 in Stockholm ( Unitary representations of nilpotent Lie groups ) . He is a fellow of the American Mathematical Society .
His son Alexander Kirillow junior is also a mathematician in the USA. He also deals with the representation theory of Lie groups.
As a schoolboy, Kirillov won several mathematical prizes in competitions, including the Mathematics Olympiad. He is the author of several popular science books.
Kirillov had a very active seminar in Moscow for 30 years. Among his students are Victor Ginzburg , the recipient of the Fields Medal Andrei Okunkow and David Kazhdan .
In 1965 he received the Moscow Mathematical Society Prize.
Fonts
- Elements of the Theory of Representations. Springer, 1976 (Russian 1972).
- Lectures on the orbit method. Graduate Studies in Mathematics, 64th American Mathematical Society, Providence, Rhode Island, 2004.
- Geometric quantization. In: Encyclopedia of Mathematical Sciences. Dynamical Systems. Vol. 4, 1990.
- Introduction to the theory of representations and noncommutative harmonic analysis. In: Encyclopedia of Mathematical Sciences. Vol. 22, 1994.
Web links
- Kirillov at the Mathematics Genealogy Project
- Homepage
- Dynkin Collection with interview
- Kirillov website
- Kirillov: Merits and demerits of the orbit method. Bulletin AMS 1999
Remarks
- ↑ originally submitted for the candidate thesis, but with it he immediately received the doctorate, which corresponds to the habilitation in the West
- ↑ It can also be applied to compact Lie groups, for example, but no longer provides a clear correspondence between irreducible representations and coadjoint orbits. See, for example, Kirillow, Bulletin of the AMS, Vol. 36, 1999, No. 4. Further applications are also discussed there.
- ↑ Coadjoint orbits correspond to homogeneous symplectic manifolds with a symmetry group , the "classical part", the "quantization" corresponds to the irreducible unitary representations of in a Hilbert space. See Kirillow, Bulletin AMS 1999.
personal data | |
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SURNAME | Kirillov, Alexander Alexandrovich |
ALTERNATIVE NAMES | Кириллов, Александр Александрович (Russian) |
BRIEF DESCRIPTION | Russian mathematician |
DATE OF BIRTH | May 9, 1936 |