Related papers: Generalized Springer theory and weight functions

A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness…

General Relativity can be formulated in terms of a spatially Weyl invariant gauge theory called Shape Dynamics. Using this formulation, we establish a "bulk/bulk" duality between gravity and a Weyl invariant theory on spacelike Cauchy…

A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur…

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This…

Based on the de Broglie-Bohm relativistic quantum theory of motion we show that the conformal formulation of general relativity, being linked with a Weyl-integrable geometry, may implicitly contain the quantum effects of matter. In this…

For a split reductive group scheme $G$ over a commutative ring $k$ with Weyl group $W$, there is an important functor $Rep(G,k) \to Rep(W,k)$ defined by taking the zero weight space. We prove that the restriction of this functor to the…

We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study in detail the effects on the corresponding associated weight…

A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power $\w_N^e$ evaluated…

We consider a generalisation of a definite integral involving the Bessel function of the first kind. It is shown that this integral can be expressed in terms of the Fox-Wright function ${}_p\Psi_q(z)$ of one variable. Some consequences of…

The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we show that in both situations, the action of…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with a help of a family of weight functions (not radial in general) is considered…

We derive an asymptotic expansion for the Weyl function of a one-dimensional Schr\"odinger operator which generalizes the classical formula by Atkinson. Moreover, we show that the asymptotic formula can also be interpreted in the sense of…

We give a self-contained account of a construction due to Rossmann which lifts Springer's action of a Weyl group on the cohomology of a Springer fiber to an action on its homotopy type. We use this construction to produce a generalization…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

In this paper, we prove a general simple relative trace formula. As an application, we prove a relative analogue of the Weyl law.

In this (partly expository) paper we show, using ideas from the theory of total positivity, how a number of properties of a semisimple group over the complex numbers can be presented purely in terms of the Weyl group. We also describe some…

In this paper, we study 2+2 direct product spacetimes sourced by separated electromagnetic and Yang--Mills fields within Weyl conformal gravity. We prove that all such configurations admit at least 2 independent, commuting non-null Killing…

It is known that signature of a Weyl group element is defined in terms of the number of its simple Weyl reflections. Actual calculations hence are not always possible especially for Weyl groups with higher order like $E_8$ Weyl group. By…

A classical theorem of Weyl states that any polynomial with an irrational coefficient other than the constant term is uniformly distributed mod 1. We prove a new function field analogue of this statement, confirming a conjecture of L\^{e},…