相关论文: A duality between Schroedinger operators on graphs…
Multi-indexed Jacobi polynomials are defined by the Wronskian of four types of eigenfunctions of a deformed P\"oschl-Teller Hamiltonian. We give a correspondence between multi-indexed Jacobi polynomials and pairs of Maya diagrams, and we…
We associate a Jacobi form over a rank s lattice to N=2, D=4 heterotic string compactifications which have s Wilson lines at a generic point in the vector multiplet moduli space. Jacobi forms of index m=1 and m=2 have appeared earlier in…
We introduce a class of Jacobi operators with discrete spectra which is characterized by a simple convergence condition. With any operator J from this class we associate a characteristic function as an analytic function on a suitable…
We discuss a functional model for multi--diagonal selfadjoint operators with almost periodic coefficients that generalizes the well known model for finite band Jacobi matrices. It give us an opportunity to construct examples of almost…
The mutually enriching relationship between graphs and matroids has motivated discoveries in both fields. In this paper, we exploit the similar relationship between embedded graphs and delta-matroids. There are well-known connections…
For any non-negative integer v we construct explicitly [v/2]+1 independent covariant bilinear differential operators from J_{k,m} x J_{k',m'} to J_{k+k'+v,m+m'}. As an application we construct a covariant bilinear differential operator…
It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such…
We prove a Schoenberg-type correspondence for non-unital semigroups which generalizes an analogous result for unital semigroup proved by Michael Sch\"urmann. It characterizes the generators of semigroups of linear maps on $M_n(C)$ which are…
Kramers-Wannier dualities in lattice models are intimately connected with symmetries. We show that they can be found directly and explicitly from the symmetry transformations of the boundary states in the underlying conformal field theory.…
This paper has been withdrawn by the author in favor of a stronger result proven by the author with R. Frank and T. Weidl in arXiv:0707.0998
We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.
The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis and Bjorner. In this…
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…
In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first…
We use the Kantor-Susskind\cite{kantsuss} model of fermions as "dumbbells" connecting points on a cubic lattice to points on its dual, to define a duality between local fermionic models invariant under a $Z_2$ gauge symmetry and models of…
We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jacobi matrix. In particular, we show how one can naturally…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the…
I study the Schroedinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics.
We obtain a Bernstein type result for entire two dimensional minimal graphs in $\mathbb{R}^{4}$, which extends a previous one due to L. Ni. Moreover, we provide a characterization for complex analytic curves.