Related papers: Connection coefficients for basic Harish-Chandra s…
Given a scheme over a field endowed with a strict normal crossings divisor, we define strongly parabolic connections, consistently with the current terminology for Higgs bundles. When the weights are rational with prescribed denominators,…
We show that the pre-factors of all terms of the one-dimensional Hubbard model correlation-function asymptotic expansions have an universal form, as the corresponding critical exponents. In addition to calculating such pre-factors, our…
This is an extended (factor 2.5) version of arXiv:math/0601371 and arXiv:0808.3486. We present new results in the theory of the classical $\theta$-functions of Jacobi: series expansions and defining ordinary differential equations (\odes).…
We study the relation between torsion tensors of principal connections on G-structures and characteristic conic connections on associated cone structures. We formulate sufficient conditions under which the existence of a characteristic…
The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight.…
In this note, introducing notions of CH module, CH morphism and CH connection, we define a meromorphic connection in the "$z$-direction" on periodic cyclic homology of an $A_\infty$ category as a connection on cohomology of a CH module.…
In this paper, we derive the first and the second variation of the energy functional for a pseudo-Finsler metric using the family of affine connections associated to the Chern connection. This opens the possibility to accomplish…
We provide a general algorithm for constructing the holographic dictionary for any asymptotically locally Lifshitz background, with or without hyperscaling violation, and for any values of the dynamical exponents $z$ and $\theta$, as well…
In his first 1958 paper on zonal spherical functions Harish-Chandra proved an extremely delicate convergence theorem which was basic to his subsequent definition of his Schwartz space and his theory of cusp forms. This paper gives…
In earlier papers [3,4,5,6] Gursey et al. showed development of a bilocal baryon-meson field from two quark-antiquark fields. The Hamiltonian in the case of vanishing quark masses was shown to have a very good agreement with experiments…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We study a connection problem between the fundamental systems of solutions at singular points $0$ and $1$ for the generalized hypergeometric equation which is satisfied by the generalized hypergeometric series ${}_nF_{n-1}$. In general, the…
We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given.…
This paper deals with differential equations of the form $$ \tau(y)- \lambda ^{2m} \varrho(x) y = 0, \quad \tau(y) =\sum_{k,\,s=0}^m(\tau_{k,\,s}(x)y^{(m-k)}(x))^{(m-s)}, $$ where $n=2m\geqslant 2$, $\lambda$ is the large complex parameter,…
The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carath\'eodory…
We prove the Farrell-Jones Conjecture for (non-connective) $A$-theory with coefficients and finite wreath products for hyperbolic groups, CAT(0)-groups, cocompact lattices in almost connected Lie groups and fundamental groups of manifolds…
We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) as a…
Value of generalized hypergeometric function at a special point is calculated. More precisely, value of certain multiple integral over vanishing cycle (all arguments collapse to unity) is calculated. The answer is expressed in terms of…
We study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus…
On a threefold with trivial canonical bundle, Kuranishi theory gives an algebro-geometry construction of the (local analytic) Hilbert scheme of curves at a smooth holomorphic curve as a gradient scheme, that is, the zero-scheme of the…