T-and Y-systems are ubiquitous structures in classical and quantum integrable systems.
They are difference equations having a variety of aspects related to commuting transfer …

We study the dilogarithm identities from algebraic, analytic, asymptotic, K-theoretic,
combinatorial and representation-theoretic points of view. We prove that a lot of dilogarithm …

Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are
specific expressions of some q-polynomials as sums of products of q-binomial coefficients …

We introduce a fermionic formula associated with any quantum affine algebra U q (XN (r).
Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable …

We review various aspects of representation theory of affine algebras at the critical level,
geometric Langlands correspondence, and Bethe ansatz in the Gaudin models. Geometric …

A bstract We show that specializations of the 4d\(\mathcal {N}= 2\) superconformal index
labeled by an integer N is given by Tr ℳ N where ℳ is the Kontsevich-Soibelman …

This is the first of a series of papers studying combinatorial (with no “subtractions”) bases
and characters of standard modules for affine Lie algebras, as well as various subspaces …

We present fermionic sum representations of the characters χ τ, s (p, p′) of the minimal M
(p, p′) models for all relatively prime integers p′> p for some allowed values of r and s …

We study the description of the SU (2), level k= 1, Wess-Zumino-Witten conformal field
theory in terms of the modes of the spin-1 2 affine primary field φα. These are shown to …

A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced,
as a generalization of the notion of principal subspaces. Bases and the graded dimensions …