A. A. Kirillov

Alexandre A. Kirillov

This issue and a part of the next one* are dedicated to Alexandre A. Kirillov—famous mathematician, MMJ editorial board member, one of the founding fathers of the Independent University of Moscow, teacher and friend—who is seventy this year.

The name of Kirillov is known to everyone who studies representation theory or uses it in one's research. He is a classical author of the subject, the creator and developer of its basic notions and methods. Kirillov's orbit method, the Kirillov–Kostant bracket, Kirillov's character formula, the Gelfand–Kirillov conjecture, the Gelfand–Kirillov dimension, Kirillov's model, are terms firmly established in the language of mathematics. Kirillov's orbit method is one of the most original and fruitful discoveries in representation theory in its hundred-plus year history. This method soon became widely popular and stimulated a flow of results that has not dried up to these days. Another fundamental direction was called to life by the seminal joint papers of Gelfand and Kirillov on the skew fields of fractions of universal enveloping algebras.

Wonderful and as always highly original results were obtained by Kirillov in the theory of infinite-dimensional Lie groups and algebras, and their representations. This work is relatively less known and should yet be carefully read and studied.

Kirillov's seminar at Moscow State University gathered for 30 years. It is with deep nostalgia that all its participants remember it. Kirillov has numerous students that were formed not only by the problems he put forward, but even more by his powerful personality. Let us mention only one item in the long list of his pupils and participants of his seminar—Andrei Okounkov, who received the Fields Medal this year. Alexander Kirillov has the gift of creating a specific atmosphere that stimulates research and has exquisite mathematical taste. All his students and friends warmly remember his out-of-the-city seminar sessions with their traditional soccer and especially volleyball, and charming charades.

Recently Kirillov has completed and published a fundamental monograph summing up the 40-year long development of the orbit method, and turned to a completely new subject. We wish him success in this new research, health, and happiness.

Yu. Ilyashenko, S. Lando, R. Minlos, G. Olshanski,
I. Shchepochkina, A. Sossinsky, M. Tsfasman, A. Vershik



* Papers by Yu. Neretin, Eu. Gutkin and S. Tabachnikov, A. Borodin and G. Olshanski will appear in the next issue.

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Moscow Mathematical Journal
is distributed by the
American Mathematical Society
for the
Independent University of Moscow

Online ISSN 1609-4514
© 2006, Independent University of Moscow

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