Related papers: Poisson Summation and Endoscopy for SU(2,1)

We provide some new sharp embeddings for p-Carleson and related measures in the unit disk of the complex plane

We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and…

The $\mathit{SU}(3)$ tensor multiplicities are piecewise polynomial of degree $1$ in their labels. The pieces are the chambers of a complex of cones. We describe in detail this chamber complex and determine the group of all linear…

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^2 taking values in a Grassmann algebra with N generating elements are described up to an equivalence transformation for N \ne 2.

The Bianchi groups ${\rm Bi}(d)={\rm PSL}(2,\mathcal{O}_d) < {\rm PSL}(2,\C)$ (where $\mathcal{O}_d$ denotes the ring of integers of $\Q (i\sqrt{d})$, with $d \geqslant 1$ squarefree) can be viewed as subgroups of ${\rm SO}(3,1)$ under the…

In this article we give a classification of the sub-groups in PSL(2,Z) and of the conjugacy classes of these sub-groups by the mean of an combinatorial invariant: some trivalent diagrams (dotted or not). We give explicit formulae enabling…

This note aims at presenting several new theoretical results for the compound Poisson point process, which follows the work of Zhang \emph{et al.} [Insurance~Math.~Econom.~59(2014), 325-336]. The first part provides a new characterization…

We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of $\mathrm{SL}(2,\mathbb{R})$.

At the beginning of this century, Langlands introduced a strategy known as \emph{Beyond Endoscopy} to attack the principle of functoriality. Altu\u{g} studied $\mathsf{GL}_2$ over $\mathbb{Q}$ in the unramified setting. The first step…

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper…

We investigate the group contraction method for various space-time groups, including SO(3)->E_2, SO(3,1)->G_3, SO(5-h,h)->P(3,1) (h=1 or 2), and its consequences for representations of these groups. Following strictly quantum mechanical…

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

A consequence of Rapinchuk et al. is that for $S$ a closed surface of genus $g\geq 2$, the set of Hitchin representations of $\pi_1(S)$ with image in $\mathrm{SL}(n,\mathbb{Q})$ is dense in the Hitchin component. We give a dynamical proof…

The character problems of SU(2) and SU(1,1) are reexamined from the standpoint of a physicist by employing the Hilbert space method which is shown to yield a completely unified treatment for SU(2) and the discrete series of representations…

We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…

A derivation of the standard symmetry and leptoquark family structure is presented that is more straightforward than a previous derivation.

We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for…

We present the derivation of the 6-dimensional Eulerian Lie group of the form SO(3,C). We describe our derivation process, which involves the creation of a finite group by using permutation matrices, and the exponentiation of the adjoint…

We provide an explicit direct integral decomposition for the tensor product representation $\pi_1\widehat{\otimes}\pi_2$ of the rank one spin group $\mathrm{Spin}(n,1)$ whenever $\pi_1$ is a unitary principal series representation and…

With the long term perspective of using quantum computers and tensor networks for lattice gauge theory simulations, an efficient method of digitizing gauge group elements is needed. We thus present our results for a handful of…