Related papers: Action integrals and infinitesimal characters

The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…

We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation \pi of GSp(4,F), where F is a…

We give a categorical description of the treatment of the !() exponential in the Geometry of Interaction system, with particular emphasis on the fact that the GoI interpretation 'forgets types'. We demonstrate that it may be thought of as a…

Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…

Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently,…

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy…

Let $E/F$ be a quadratic extension of finite fields. By a result of Gow, an irreducible representation $\pi$ of $G = {\rm GL}_n(E)$ has at most one non-zero $H$-invariant vector, up to multiplication by scalars, when $H$ is ${\rm GL}_n(F)$…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

Let G be a classical p-adic group and $(\psi ,\epsilon)$ the Langlands parameter of an irreducible supercuspidal representation of a Levi subgroup of G. Using data from $(\psi ,\epsilon)$, we determine explicitly the intertwining algebra of…

An oscillator group $G$ is a semidirect product of a Heisenberg group with a one-parameter group. In this article we construct Olshanski semigroups for infinite-dimensional oscillator groups. These are complex involutive semigroups which…

In this note, we study an invariant associated to the zeros of the moment map generated by an action form, the infinitesimal index. This construction will be used to study the compactly supported equivariant cohomology of the zeros of the…

Let $G$ be a non-compact simple Lie group with Lie algebra $\mathfrak{g}$. Denote with $m(\mathfrak{g})$ the dimension of the smallest non-trivial $\mathfrak{g}$-module with an invariant non-degenerate symmetric bilinear form. For an…

Let $F$ be a non-Archimedean local field and let $\mathcal{O}_{F}$ be its ring of integers. The orbit of an irreducible representation $\rho$ of $\mathrm{GL}_n(\mathcal{O}_F)$ is a conjugacy class in $\mathfrak{gl}_n(\mathcal{O}_F)$…

If a finite group $A$ acts coprimely as automorphisms on a finite group $G$, then the $A$-invariant Brauer $p$-blocks of $G$ are exactly those that contain $A$-invariant irreducible characters.

Let $\pi$ be an irreducible cuspidal representation of $\mathrm{GL}_{kn}\left(\mathbb{F}_q\right)$. Assume that $\pi = \pi_{\theta}$, corresponds to a regular character $\theta$ of $\mathbb{F}_{q^{kn}}^{*}$. We consider the twisted Jacquet…

Let $G$ be a finite simple group of Lie type, and let $\pi_G$ be the permutation representation of $G$ associated with the action of $G$ on itself by conjugation. We prove that every irreducible representation of $G$ is a constituent of…

Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a…

Let G be a locally compact group, M(G) denote its measure algebra and L^1(G) denote its group algebra. Also, let pi:G->U(H) be a strongly continuous unitary representation, and let CB^{sigma}(B(H)) be the space of normal completely bounded…

Let $\mathfrak{h}_3$ be the Heisenberg algebra and let $\mathfrak g$ be the 3-dimensional Lie algebra having $[e_1,e_2]=e_1\,(=-[e_2,e_1])$ as its only non-zero commutation relations. We describe the closure of the orbit of a vector of…