Related papers: Integrals of motion from quantum toroidal algebras
We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function…
We call a Lebesgue-Feynman measure (LFM) any generalized measure (distribution in the sense of Sobolev and Schwartz) on a locally convex topological vector space E which is translation invariant. In the present paper, we investigate…
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…
Almost integral TQFTs were introduced by Gilmer [Duke Math. J. 125 (2004) 389--413]. The aim of this paper is to modify the TQFT of the category of extended 3-cobordisms given by Turaev (in his book: Quantum invariants of knots and…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…
We interpret a formula established by Lapid-M\'{\i}nguez on real regular representations of ${\rm GL}_n$ over a local non-archimedean field as a matrix determinant. We use the Lewis Carroll determinant identity to prove new relations…
We define a path integral over Dirac operators that averages over noncommutative geometries on a fixed graph, as the title reveals, using quiver representations. We prove algebraic relations that are satisfied by the expectation value of…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
We employ an isometry group invariants approach to study Killing tensors of valence three defined in the Euclidean plane. The corresponding invariants are found to be homogeneous polynomials of the parameters of the vector space of the…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…
The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so-called Fateev, quantum AKNS, paperclip and KdV integrable structures, they are…
We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras respectively. We then relate a construction of Efimov in the context of…
An elliptic version of quantum groups is proposed. It comes form the quantization of the Knizhnik-Zamolodchikov- Bernard equation on the torus. The relation with elliptic IRF models is explained.
This paper initiates the study by analytic methods of the generalized principal series Maass forms on $GL(3)$. These forms occur as an infinite sequence of one-parameter families in the two-parameter spectrum of $GL(3)$ Maass forms,…
We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…
A plane algebraic curve whose Newton polygone contains d lattice points can be given by d points it passes through. Then the coefficients of its equation Poisson commute having been regarded as functions of coordinates of those points. It…
We review some classical and modern aspects of hypergeometric differential equations, including $A$-hypergeometric systems of Gel'fand, Graev, Kapranov and Zelevinsky. Some recent advances in this theory, such as Euler-Koszul homology, rank…
We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- $\gtsl_{n+1}$-modules. The formulas are closely related to WZNW model at a…