Alexandre Kirillov

Alexander Alexandrovich Kirillov (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 U.S..

Kirillov studied at the Moscow State University in Moscow, where he received his doctorate in 1962 with Israel Gelfand on Unitary representations of nilpotent Lie groups (Russian Mathematical Surveys Bd.17, 1962, p.57 -110 ). After that, he was a professor at the Moscow State University. In 1994 he was Francis J. Carey Professor of Mathematics at the University of Pennsylvania.

Kirillov is known for the orbit method in representation theory of Lie groups. Kirillov examined initially only nilpotent Lie groups, where he showed that the irreducible unitary representations (up to unitary equivalence ) classified by the " orbit " of the images of the dual Lie algebra ( koadjungierte orbits) of. From Bertram Kostant, Louis Auslander, Lajos Pukánszky and others, the orbit method was extended to solvable Lie groups. From its orbit method, he also launched a formula for the characters of the irreducible representations of the Lie group from ( Kirillov character formula ).

Kirillov includes in its orbit method, a version of geometric quantization.

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 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 Kirillov junior is also mathematicians in the United States. He also deals with the representation theory of Lie groups.

Kirillov won already as a student several mathematical Prices in competitions, including the Mathematical Olympiad. He is the author of several popular science books.

Kirillov had for 30 years a very active seminar in Moscow. Among his students Victor Ginzburg, the winner of the Fields Medal Andrei Okunkow and David Kazhdan.

In 1965 he was awarded the prize of the Moscow Mathematical Society.

Writings

• Elements of the Theory of Representations. Springer, 1976 ( Russian 1972).
• Lectures on the orbit method. Graduate Studies in Mathematics, 64 American Mathematical Society, Providence, Rhode Iceland, 2004.
• Geometric Quantization. In: Encyclopedia of Mathematical Sciences. Dynamical Systems. Volume 4, 1990.
• Introduction to the theory of representations and Noncommutative harmonic analysis. In: Encyclopedia of Mathematical Sciences. Bd.22, 1994.