Jordan-Schwinger representations and factorised Yang-Baxter operators.
Level set structure of an integrable cellular automaton.
Limits of Gaudin systems: classical and quantum cases.
Miura opers and critical points of master functions
Critical points of a master function associated to a simple Lie algebra come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...
Modelli di Spin deterministici con comportamento vetroso
New adventures in the land of -analogues (Yang-Baxter equations). (Nouvelles aventures au pays des -analogues (équation de Yang-Baxter).)
Numerical study of the 6-vertex model with domain wall boundary conditions
A Markov process converging to a random state of the 6-vertex model is constructed. It is used to show that a droplet of c-vertices is created in the antiferromagnetic phase and that the shape of this droplet has four cusps.
On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the number of fully packed loop configurations with a fixed associated matching.
Promotion operator on rigged configurations of type .
Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns.
Quantum curve in -oscillator model.
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quantum integrable model of an arrangement of hyperplanes.
Quantum relativistic Toda chain.
Quantum relativistic Toda chain at root of unity: isospectrality, modified -operator, and functional Bethe ansatz.
Several identities in statistical mechanics.
Smallness problem for quantum affine algebras and quiver varieties
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Solutions to the XXX type Bethe ansatz equations and flag varieties
We consider a version of the A N Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the sl N+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems B N and...
Solvable lattice model and representation theory of quantum affine algebras.