In a cycle of joint works with A. Yu. Okounkov, a new class of symmetric functions (interpolation Schur and Jack polynomials) was studied. The results were applied in representation theory of infinite-dimensional groups. In a cycle of works with A. M. Borodin, S. V. Kerov, and A. M. Vershik, the problem of harmonic analysis on the infinite symmetric group and the infinite-dimensional unitary group was stated and studied. A link with random matrix theory was found. As an application, a proof of the recent conjecture by Baik, Deift, and Johansson on coincidence of certain asymptotic characteristics of random permutations and random matrices was obtained (joint result with A. M. Borodin and A. Yu. Okounkov).
Main publications:
Okounkov A., Olshanski G. Asymptotics of Jack polynomials as the number of variables goes to infinity // Intern. Math. Res. Notices, 1998, 13, 641–682.
Borodin A., Olshanski G. Distributions on partitions, point processes, and the hypergeometric kernel // Comm. Math. Phys., 2000, 211, 335–358.
Borodin A., Okounkov A., Olshanski G. Asymptotics of Plancherel measures for symmetric groups // J. Amer. Math. Soc., 2000, 13, 481–515.
