Related papers: Phase retrieval for nilpotent groups

If $G$ is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to infinity. Whereas random groups are quotients…

An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…

Let $G(\mathbb{R})$ be a real reductive group. Suppose $\pi$ is an irreducible representation of $G(\mathbb{R})$ having a Whittaker model, and consider three invariants of $\pi$ related to nilpotents elements of the Lie algebra of $G$ (or…

We establish a general CCR (liminarity) property for uniformly bounded irreducible representations of nilpotent Lie groups on reflexive Banach spaces, extending the well known property of unitary irreducible representations of these groups…

It is proved that the orbit space of an irreducible representation of a simple connected compact Lie group of type B, C, or D can be a smooth manifold only in two cases.

We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite p-groups of nilpotency class less than p. This allows us to unify and generalize a number of existing enumerative results, and to…

Let $G$ be a real reductive linear group in the Harish-Chandra class. Suppose that $P$ is a parabolic subgroup of $G$ with Langlands decomposition $P=MAN$. Let $\pi$ be an irreducible representation of the Levi factor $L=MA$. We give…

The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…

We consider the class of groups called identity excluding which has the property that any non-trivial irreducible unitary representation restricted to a dense subgroup does not weakly contain the trivial representation. For adapted and…

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies a given polynomial identity $r(t)=0$. For the polynomial $r=t^n-1$ we obtain results on the nilpotency of Lie algebras admitting a…

Let G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classified. We describe a simple algorithm for finding a…

Because of the importance of unitarity in quantum physics, work on the representations of the de Sitter group has focussed on the unitary case, which necessarily means infinite dimensional matrices for this non-compact group. Here we…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

A result of D. Segal states that every complex irreducible representation of a finitely generated nilpotent group $G$ is monomial if and only if $G$ is abelian-by-finite. A conjecture of A. N. Parshin, recently proved affirmatively by I.V.…

We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.

We study nonlinear determination problems in Hilbert spaces in which inner products are observed up to prescribed rotations in the complex plane. Given a Hilbert space $H$ and a subset $\Theta$ of the unit circle $\mathbb{T}$, we say that a…

We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite…