The Institute for Theoretical and Experimental Physics (ITEP) is internationally recognized for achievements in various branches of theoretical physics. For many years, the seminars at ITEP have been among the main centers of scientific life in Moscow. This volume is a collection of articles by participants of the seminar on mathematical physics that has been held at ITEP since 1983. This is the second such collection; the first was published in the same series, AMS Translations, Series 2, vol. 191. The papers in the volume are devoted to several mathematical topics that strongly influenced modern theoretical physics. Among these topics are cohomology and representations of infinite Lie algebras and superalgebras, Hitchin and Knizhnik-Zamolodchikov-Bernard systems, and the theory of $D$-modules. The book is intended for graduate students and research mathematicians working in algebraic geometry, representation theory, and mathematical physics.
Hecke-Tyurin parametrization of the Hitchin and KZB systems by B. Enriquez and V. Rubtsov Combinatorics and geometry of higher level Weyl modules by B. Feigin, A. N. Kirillov, and S. Loktev Cosh-Gordon equation and quasi-Fuchsian groups by V. V. Fock On a class of representations of quantum groups and its applications by A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin On syzygies of highest weight orbits by A. L. Gorodentsev, A. S. Khoroshkin, and A. N. Rudakov On finest and modular t-stabilities by A. L. Gorodentsev and S. A. Kuleshov Hochschild homology and Gabber's theorem by D. Kaledin Method of projections of Drinfeld currents by S. Khoroshkin and S. Pakuliak On rational and elliptic forms and Painleve VI equation by A. Levin and A. Zatov Determinantal point processes and fermionic Fock space by Y. A. Neretin On adelic model of boson Fock space by Y. A. Neretin Hypercomplex manifolds with trivial canonical bundle and their holonomy by M. Verbitsky.