nLab Alexandre Kirillov

Not to be confused with Alexander Kirillov, Jr..

Alexandre Aleksandrovich Kirillov (Александр Александрович Кириллов) is a professor of mathematics at the University of Pennsylvania. He invented the orbit method in representation theory, developed in other flavours also by Kostant and Souriau. He was a student of Israel Gelfand and they together lead a famous journal Functional Analysis and its Applications.

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Selected writings

On superalgebra and supergeometry (Grassmann algebra, super vector spaces, supermanifolds, super Lie algebras, super Lie groups, …):

• Felix A. Berezin (edited by Alexandre A. Kirillov): Introduction to Superanalysis, Mathematical Physics and Applied Mathematics 9, Springer (1987) [doi;10.1007/978-94-017-1963-6_8]

On geometric quantization:

• Alexandre Kirillov: Geometric quantization, in: Dynamical systems IV, Encyclopedia of Mathematical Sciences 4, Springer (1990) 137-172 [doi:10.1007/978-3-662-06793-2_2]

On Reshetikhin-Turaev theory constructing modular functors from modular tensor categories:

• Bojko Bakalov, Alexandre Kirillov: Lectures on tensor categories and modular functors, University Lecture Series 21, Amer. Math. Soc. (2001) [webpage, ams:ulect/21, pdf]

On the orbit method:

• Alexandre Kirillov: Lectures on the Orbit Method, Graduate Studies in Mathematics 64, American Mathematical Society (2004) [doi:10.1090/gsm/064]

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