Related papers: Determinant representations for form factors in qu…

We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of…

An orthogonal basis of the Hilbert space for the quantum spin chain associated with the su(3) algebra is introduced. Such kind of basis could be treated as a nested generalization of separation of variables (SoV) basis for high-rank quantum…

To a finite dimensional representation of a complex Lie group $G$, an associative algebra of adjoint covariant polynomial maps from the direct sum of $m$ copies of the Lie algebra $\mathfrak{g}$ of $G$ into an algebra of complex matrices is…

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…

We study the algebra of invariant representative functions over the N-fold Cartesian product of copies of a compact Lie group G modulo the action of conjugation by the diagonal subgroup. We construct a basis of invariant representative…

We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables…

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A-infinity-algebras, introduced in "Modular operads and…

{Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we…

A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…

We list solutions of the graded reflection equation associated with the fundamental vector representation of the quantum supergroup of GL-type.

We study a certain type of multiple commutation relations of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_N)$. We show that all the coefficients in the multiple commutation relations between the $L$-operator elements are given in…

We establish the basics of the Bethe ansatz for the Gaudin model associated to the Lie superalgebra gl(m|n). In particular, we prove the completeness of the Bethe ansatz in the case of tensor products of fundamental representations.

We consider the Lieb-Liniger model for a gas of bosonic $\delta-$interacting particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic limit of the form factors of the density operator between finite entropy eigenstates…

We classify the possibilities for the fixed field of the kernel of an irreducible three-dimensional Artin representation of $\Q$ with solvable image ramified at one prime by using the classification of the finite irreducible subgroups of…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

A new two-parameter integrable model with quantum superalgebra $U_q[gl(3|1)]$ symmetry is proposed, which is an eight-state electron model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping.…

Conformal blocks and their AGT relations to LMNS integrals and Nekrasov functions are best described by "conformal" (or Dotsenko-Fateev) matrix models, but in non-Gaussian Dijkgraaf-Vafa phases, where different eigenvalues are integrated…

Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p > 3. We classify all irreducible modules of g, and give the character formulae for irreducible modules.

In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we…

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a…