Related papers: Norms of eigenfunctions to trigonometric KZB opera…
The eigenvectors of the osp(1|2) invariant Gaudin hamiltonians are found using explicitly constructed creation operators. Commutation relations between the creation operators and the generators of the loop superalgebra are calculated. The…
We propose a new method of diagonalization of hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on Wakimoto modules over affine algebras at the critical level. We construct eigenvectors of these…
The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of…
The problems connected with Gaudin models are reviewed by analyzing model related to the trigonometric osp(1|2) classical r-matrix. The eigenvectors of the trigonometric osp(1|2) Gaudin Hamiltonians are found using explicitly constructed…
The irrelevant composite operator $T\bar{T}$, constructed from components of the stress-energy tensor, exhibits unique properties in two-dimensional quantum field theories and represents a distinctive form of integrable deformation.…
We examine the commuting elements $\theta_i=\sum_{j\neq i} \frac{s_{ij}}{z_i-z_j}$, $z_i\neq z_j$, $s_{ij}$ the transposition swapping $i$ and $j$, and we study their actions on irreducible $S_n$ representations. By applying Schur-Weyl…
In this article, we construct operator models for meromorphic functions of bounded type on Krein spaces. This construction is based on certain reproducing kernel Hilbert spaces which are closely related to model spaces. Specifically, we…
We implement the Bethe anstaz method for the elliptic quantum group $E_{\tau,\eta}(A_2^{(2)})$. The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence relation. We also give the…
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…
We give a construction of creation operators responsible for appearance of Bethe vectors with the same eigenvalues of the transfer-matrix for the inhomogeneous arbitrary spin XXZ model at roots of unity with particular quasiperiodic…
To any simple Lie algebra $\mathfrak g$ and automorphism $\sigma:\mathfrak g\to \mathfrak g$ we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of $U(\mathfrak g)^{\otimes N}$ generated by a hierarchy of…
We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
We consider a tensor product of a Verma module and the linear representation of $sl(n+1)$. We prove that the corresponding phase function, which is used in the solutions of the KZ equation with values in the tensor product, has a unique…
For fully nonlinear $k$-Hessian operators on bounded strictly $(k-1)$-convex domains $\Omega$ in ${\mathbb R}^N$, a characterization of the principal eigenvalue associated to a $k$-convex and negative principal eigenfunction will be given…
The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…
Let $V$ be a vertex operator superalgebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra $V^{\otimes k}$. In this paper, we construct an explicit…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…
Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra…