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Regular version of the site

HSE – Skoltech International Laboratory of Representation Theory and Mathematical Physics

Lectures on Dispersionless Integrable Hierarchies

Takebe T.

Tokyo: Research Center for Mathematical Physics, Rikkyo Universty, 2014.

Crystals and monodromy of Bethe vectors

Rybnikov L. G., Halacheva I., Kamnitzer J. et al.

Duke Mathematical Journal. 2020. Vol. Advanced publication. P. 1-83.

Book chapter
Links Between Quantum Chaos and Counting Problems

Orlov A. Y.

In bk.: Geometric Methods in Physics XXXVI. Workshop and Summer School, Białowieża, Poland, 2017. Contains papers. Springer, 2019. P. 355-373.

Working paper
Dual description of eta-deformed OSP sigma-models I

Alfimov M., Feigin B. L., Hoare B. et al.

hep-th. arXiv. Cornell University, 2020. No. 2003.xxxxx.

The main objective of the laboratory is to develop a common approach to a variety of issues at the interface between the theory of integrable systems and representation theory of quantum and infinite-dimensional groups and algebras.

Research are conducted in several inter-related directions and involves close cooperation between mathematicians and mathematical physicists.

These areas include:

  1. Representation theory of vertex algebras and of their quantum analogs (in particular, double affine quantum groups and q-W-algebras);
  2. Developing methods of vertex algebras in low-dimensional Topology and in Quantum Field Theory;
  3. Quantum cohomology of moduli spaces of sheaves and related Geometric Representation Theory and Integrable Systems (in particular, Toda and Calogero systems and their generalizations);
  4. Geometric Langlands correspondence;
  5. Cluster structures on moduli spaces, their geometry and combinatorics;
  6. Combinatorics of Kashiwara crystals in quantum integrable systems.