Related papers: Generalized Green functions and unipotent classes …
We state a conjecture which gives a combinatorial parametrization of the irreducible tempered representations with real central character of a graded Hecke algebra with unequal labels, associated to a root sytem of type B or C. This…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
We present a characteristic initial value approach to calculating the Green function of the Regge-Wheeler and Zerilli equations. We combine well-known numerical methods with newly derived initial data to obtain a scheme which can in…
In this paper, we generalize results of Bruinier on automorphic Green functions on Hilbert modular surfaces to arbitrary ideals. For instance, we compute the Fourier expansion of the unregularized Green functions, use it to regularize them,…
We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a…
Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we clarify the combinatorial interpretation of certain…
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the…
We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the…
We continue the attempt to develop a theory of character sheaves on a not necessarily connected reductive algebraic group. In this paper we introduce and study the generalized Green functions.
We show that on any abelian scheme over a complex quasi-projective smooth variety, there is a Green current for the zero-section, which is axiomatically determined up to $\partial$ and $\bar\partial$-exact differential forms. This current…
Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…
It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
We propose a general method to obtain the scalar worldline Green function on an arbitrary 1D topological space, with which the first-quantized method of evaluating 1-loop Feynman diagrams can be generalized to calculate arbitrary ones. The…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We complete the determination of the generalised Springer correspondence for connected reductive algebraic groups, by proving a conjecture of Lusztig on the last open cases which occur for groups of type $E_8$.
We present a generalized version of classical geometric invariant theory \`a la Mumford where we consider an affine algebraic group $G$ acting on a specific affine algebraic variety $X$. We define the notions of linearly reductive and of…
We present a new method for calculating the Green functions for a lattice scalar field theory in $D$ dimensions with arbitrary potential $V(\phi)$. The method for non-perturbative evaluation of Green functions for $D \! = \! 1$ is…
This article is about the $\mathbb{Z}^d$-periodic Green function $G_n(x,y)$ of the multiscale elliptic operator $Lu=-{\rm div}\left( A(n\cdot) \cdot \nabla u \right)$, where $A(x)$ is a $\mathbb{Z}^d$-periodic, coercive, and H\"older…