We review recent results in the matrix model approach to the 2-d noncritical string theory compactified in time, in the phase of condensation of the world sheet vortices (above the Berezinski-Kosterlitz-Thouless phase transition) [1, 2, 3]. This phase is known to describe strings on the 2-d black hole background, due to the conjecture of V.Fateev, A. and Al.Zamolodchikov. The corresponding matr...

In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the SU(2)k ⊗ SU(2)l/SU(2)k+l coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the c...

Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic boundary fields is constructed. It found that transfer matrix this model can be factorized as product those two open staggered anisotropic XXZ chains. Based on identity, eigenvalues and Bethe ansatz equations are derived via off-diagonal ansatz.

We review the separation of variables for the Kowalevski top and for its generalization to the algebra o(4). We notice that the corresponding separation equations allow an interpretation of the Kowalevski top as a B (1) 2 integrable lattice. Consequently, we apply the quadratic r-matrix formalism to construct a new 2× 2 Lax matrix for the top, which is responsible for its separation of variable...

In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m) × so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Bessel and Whittaker func...

It is shown that time-harmonic hypersurface motions in various, conformally flat, N -dimensional manifolds admit a multilinear description, L̇ = {L,M1, · · · ,MN−2}, automatically generating infinitely many conserved quantities, as well as leading to new (integrable) matrix equations. Interestingly, the conformal factor can be changed without changing L. ∗ Heisenberg Fellow On leave of absence f...

We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta = 1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the...