@inproceedings{1e611401f1ce4ab0a7ae1f130f0acedd,
title = "Fermionic spectra in integrable models",
abstract = "This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between fermionic formulas for the graded dimensions of the spaces of conformal blocks of WZW theories, quantum cluster algebras, discrete integrable noncommutative evolutions and difference equations.",
keywords = "Discrete integrable systems, Fermionic character formulas, Fusion products",
author = "Rinat Kedem",
note = "Funding Information: Acknowledgements. The author would like to express her gratitude to her advisor B.M. McCoy, with whom the original formulation of the physical interpretation of conformal partition functions and their fermionic expressions was made; To M. Jimbo, T. Miwa for their patient mentorship over many years; to them as well as B. Feigin and E. Ardonne, with whom she first worked on fusion products; and most especially to P. Di Francesco for an on-going illuminating collaboration. The author thanks S. Fomin, H. Nakajima, N. Reshetikhin for their kindness and for helpful discussions related to this work over the years. This work has been supported by the National Science foundation through several grants, most recently NSF DMS grant 1100929. Publisher Copyright: {\textcopyright} ICM 2014.All rights reserved.; 2014 International Congress of Mathematicans, ICM 2014 ; Conference date: 13-08-2014 Through 21-08-2014",
year = "2014",
language = "English (US)",
series = "Proceeding of the International Congress of Mathematicans, ICM 2014",
publisher = "KYUNG MOON SA Co. Ltd.",
pages = "1141--1158",
editor = "Jang, {Sun Young} and Kim, {Young Rock} and Dae-Woong Lee and Ikkwon Yie",
booktitle = "Invited Lectures",
}