Related papers: Remarks on computing Green functions
In a previous paper, "Generalized Green functions and unipotent classes for finite reductive groups, I", we have determined certain unknown scalars involved in the algorithm of computing generalized Green functions in the case of SL_n. In…
Lusztig's algorithm of computing generalized Green functions of reductive groups involves an ambiguity of certain scalars. In this paper, for reductive groups of classical type with arbitrary characteristic, we determine those scalars…
Based on results of Digne-Michel-Lehrer (2003) we give two formulae for two-variable Green functions attached to Lusztig induction in a finite reductive group. We present applications to explicit computation of these Green functions, to…
The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the F_q structure of irreducible local systems on unipotent classes on G. In this paper, we determine such…
In this paper, we consider the set of r-symbols in a full generality. We construct Hall-Littlewood functions and Kostka functions associated to those r-symbols. We also discuss a multi-parameter version of those functions. We show that…
The 2-parameter Green functions occur as a crucial ingredient in the character formula for Lusztig induction in finite reductive groups. Still, very little is known about these functions, in particular in the case of groups arsing from…
A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…
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…
Explicit form of two-point and three-point Sp(2M) invariant Green functions is found.
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
We develop calculational method for fermionic Green functions in the framework of Grassmann higher-order tensor renormalization group. The validity of the method is tested by applying it to three-dimensional free Wilson fermion system. We…
In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent…
In this paper we prove a uniform estimate for the gradient of the Green function on a closed Riemann surface, independent of its conformal class, and we derive compactness results for immersions with L2-bounded second fundamental form and…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…