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.
|Original language||English (US)|
|Title of host publication||Proceedings of the International Congress of Mathematicians---Seoul 2014. Vol. III|
|Publisher||Kyung Moon Sa, Seoul|
|Number of pages||18|
|State||Published - 2014|