Related papers: Gaudin's model and the generating function of the …

We study the eigenvalue problem of the squared Pauli-Lubanski vector, W^{2}, in the Spinor-Vector representation space and derive from it that the -s(s+1)m^{2} subspace with s=3/2, i.e. spin 3/2 in the rest frame, is pinned down by the one…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

We introduce and study a class of two-dimensional integrable quantum field theories that carry an internal $\mathbb{Z}_n$ structure. These models extend factorised scattering beyond the conventional framework, featuring both the usual…

We study the geometry of compact geodesic spaces with trivial first Betti number admitting large finite groups of isometries. We show that if a finite group $G$ acts by isometries on a compact geodesic space $X$ whose first Betti number…

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra $U(\g)$ of a semisimple Lie algebra $\g$. This family is parameterized by collections of pairwise…

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…

We consider the Frobenius algebra of functions on the critical set of the master function of a weighted arrangement of hyperplanes in $\C^k$ with normal crossings. We construct two potential functions (of first and second kind) of variables…

We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining…

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum…

The $s$-point correlation function of a Gaussian Hermitian random matrix theory, with an external source tuned to generate a multi-critical singularity, provides the intersection numbers of the moduli space for the $p$-th spin curves…

In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to $N-1$ spins $\frac{1}{2}$, contains one arbitrarily large spin $S$.…

Answering a question posed by Adam Epstein, we show that the collection of conjugacy classes of polynomials admitting a parabolic fixed point and at most one infinite critical orbit is a set of bounded height in the relevant moduli space.…

We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst…

We introduce a framework to study the random entire function $\zeta_\beta$ whose zeros are given by the Sine$_\beta$ process, the bulk limit of beta ensembles. We present several equivalent characterizations, including an explicit power…

We study generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construction of epimorphisms from the generalized Whittaker model…

In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…

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…

The Gaudin models based on the face-type elliptic quantum groups and the $XYZ$ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding…

Recently, Bazhanov and Sergeev have described an Ising-type integrable model which can be identified as a $\sinh$-Gordon-type model with an infinite number of states but with a real parameter $q$. This model is the subject of Sklyanin's…

Let $M$ be a 2-disk or a cylinder, and $f$ be a smooth function on $M$ with constant values at $\partial M$, devoid of critical points in $\partial M$, and exhibiting a property wherein for every critical point $z$ of $f$ there is a local…