Related papers: Generalized Green functions and unipotent classes …
We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group will not be…
Inspired by the theory of Hodge correlators due to Goncharov and by the plectic principle of Nekov\'a\v{r} and Scholl, we construct higher plectic Green functions and give a higher order generalization of Hecke's formula for abelian…
Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function $G_s(z_1,z_2)$ for the elliptic modular group at positive integral spectral parameter $s$ are given by logarithms of algebraic…
The effects of quantum fluctuations in fields confined by background configurations may be simply and transparently computed using the Green's function approach pioneered by Schwinger. Not only can total energies and surface forces be…
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole spacetime, i.e., a $(1+d)$-spacetime with $d\geq3$ which presents a solid angle deficit. Our result is…
We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
We show that the n-fold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model, as well as various other n-fold integrals of the "Ising class", or n-fold integrals from enumerative combinatorics, like lattice Green…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We look at estimates for the Green's function of time-fractional evolution equations of the form $D^{\nu}_{0+*} u = Lu$, where $D^{\nu}_{0+*}$ is a Caputo-type time-fractional derivative, depending on a L\'evy kernel $\nu$ with variable…
Let G be a connected reductive algebraic group over an algebraically closed field k. We consider the strata in G defined by Lusztig as fibers of a map given in terms truncated induction of Springer representations. We extend to arbitrary…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
In a remarkable series of works, Guo, Phong, Song, and Sturm have obtained key uniform estimates for the Green's functions associated with certain K\"ahler metrics. In this note, we broaden the scope of their techniques by removing one of…
In this paper, we compute the Clebsch-Gordan formulae and the Green rings of connected pointed tensor categories of finite type.
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…
In the present paper we establish sharp pointwise estimates on the polyharmonic Green function and its derivatives in an arbitrary bounded open set.
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
For $p_1,...,p_n>0$, let $\mathbb E=\{z\in\mathbb C^n:\sum_{j=1}^n|z_j|^{2p_j}<1\}$ be a complex ellipsoid. We present effective formulas for the generalized M\"obius and Green functions $m_{\mathbb E}(A,\cdot)$, $g_{\mathbb E}(A,\cdot)$ in…