Related papers: Bases of Bethe Vectors and Difference Equations wi…
Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if L is a component of the (stable)…
We obtain a determinant representation of normalized scalar products of on-shell and off-shell Bethe vectors in the inhomogeneous 8-vertex model. We consider the case of rational anisotropy parameter and use the generalized algebraic Bethe…
Given a block of a finite group, any source algebra has a basis invariant under the multiplicative actions of the defect group. Is such a basis a characteristic biset of the block fusion system? If the basis can be chosen to consist…
In this paper we compare two constructions of weight functions (off-shell Bethe vectors) for the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_N)$. The first construction comes from the algebraic nested Bethe ansatz. The second one is…
We study solutions of the Bethe Ansatz equation related to the trigonometric Gaudin model associated to a simple Lie algebra g and a tensor product of irreducible finite-dimensional representations. Having one solution, we describe a…
In the representation theory of finite-dimensional algebras, the study of projective presentations of maximal rank is closely related to the study of generically $\tau$-regular irreducible components of varieties of modules over such…
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various…
Bit-vectors, which are integers in a finite number of bits, are ubiquitous in software and hardware systems. In this work, we consider the satisfiability modulo theories (SMT) of bit-vectors. Unlike normal integers, the arithmetics of…
We study the $\mathfrak{gl}_{m|n}$ XXX spin chains defined on tensor products of highest $\mathfrak{gl}_{m|n}$-modules. We show that the on-shell Bethe vectors are eigenvectors of higher transfer matrices and compute the corresponding…
Schur modules give the irreducible polynomial representations of the general linear group $\mathrm{GL}_t$. Viewing the symmetric group $\mathfrak{S}_t$ as a subgroup of $\mathrm{GL}_t$, we may restrict Schur modules to $\mathfrak{S}_t$ and…
We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique…
The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $\lambda$ over such a group as the tensor…
We compute an universal weight function (off-shell Bethe vectors) in any representation with a weight singular vector of the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_N)$ applying the method of projections of Drinfeld currents…
In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective…
We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda, the weight subspace of weight $\lambda$ of the tensor product of k polynomial irreducible gl_N-modules with highest weights…
In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of…
We obtain determinant representations for the form factors of the monodromy matrix entries in quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. These representations can be…
We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)\oplus gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase…
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…
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.