Pavel Etingof

Learn More
Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also(More)
In the paper [Dr3] V.Drinfeld formulated a number of problems in quantum group theory. In particular, he raised the question about the existence of a universal quantization for Lie bialgebras, which arose from the problem of quantization of Poisson Lie groups. When the paper [KL] appeared Drinfeld asked whether the methods of [KL] could be useful for the(More)
The author considers an elliptic analogue of the Knizhnik-Zamolodchikov equations – the consistent system of linear differential equations arising from the elliptic solution of the classical Yang-Baxter equation for the Lie algebra slN . The solutions of this system are interpreted as traces of products of intertwining operators between certain(More)
1.1. Classical r-matrices. In the early eighties, Belavin and Drinfeld [BD] classified nonskewsymmetric classical r-matrices for simple Lie algebras. It turned out that such r-matrices, up to isomorphism and twisting by elements from the exterior square of the Cartan subalgebra, are classified by combinatorial objects which are now called Belavin-Drinfeld(More)
These are the notes of my talk at the conference “Double affine Hecke algebras and algebraic geometry” (MIT, May 18, 2010). The goal of this talk is to discuss some results and conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the representation theory for affine(More)
We introduce a class of multidimensional Schrödinger operators with elliptic potential which generalize the classical Lamé operator to higher dimensions. One natural example is the Calogero–Moser operator, others are related to the root systems and their deformations. We conjecture that these operators are algebraically integrable, which is a proper(More)
The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation. This generalization was introduced by Gervais, Neveu, and Felder. Unlike the QYB equation, the QDYB equation is not an algebraic but a difference equation, with respect to a matrix function rather than a matrix. The QDYB equation and its(More)
We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i. e. for fusion categories), obtained recently in our joint work with D. Nikshych. In particular, we generalize to the categorical setting the Hopf and quasi-Hopf algebra freeness theorems due to Nichols–Zoeller and(More)