相关论文: Hessenberg Input Normal Representations

We discuss a fine tuning of the co- and contra-variant transforms through construction of specific fiducial and reconstructing vectors. The technique is illustrated on three different forms of induced representations of the Heisenberg…

We introduce the term "protonormal" to refer to a subgroup H of a group G such that for every x in G the subgroups x^{-1}Hx and H commute as sets. If moreover (G,H) is a Hecke pair we show that the Hecke algebra H(G,H) is generated by the…

Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…

In this paper we construct two types of Hessenberg matrices with the properties that every weighted isobaric polynomial (WIP) appears as a determinant of one of them, and as the permanent of the other. Every integer sequence which is…

The Hessian map is the rational map that sends a homogeneous polynomial to the determinant of its Hessian matrix. We prove that the Hessian map is birational on its image for ternary forms of degree $d\ge 4$, $d\neq 5$, by considering the…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence…

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can…

Let $A$ be a commutative noetherian ring and $I$ an ideal in $A$. We characterize algebraically when all the minimal primes of the associated graded ring $G_I A$ contract to minimal primes of $A/I$. This, applied to intersection theory,…

Let $\mathbb{N}$ be the set of all nonnegative integers. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let $R_S(n)$ denote the number of solutions of the equation $n=s+s'$, $s, s'\in S$, $s<s'$. In this paper, we determine the…

We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for…

The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized with a Hessenberg form. In…

A $*$-bimodule for a unital $*$-algebra $A$ is an $A$-bimodule $X$ which is a vector space with involution $x\mapsto x^+$ satisfying $(a\cdot x\cdot b)^+=b^+\cdot x^+\cdot b^+$ for $x\in X$ and $a,b\in A$. An algebraic model for…

Determining whether an irreducible representation of a group (or $*$-algebra) admits a non-degenerate invariant, positive-definite Hermitian form is an important problem in representation theory. In this paper, we study a related notion:…

Let $\mathbf{G}$ be a split algebrac group of type $E_n$ defined over a $p$-adic field. This group contains a dual pair $G \times G'$ where one of the groups is of type $G_2$. The minimal representation of $\mathbf{G}$, when restricted to…

In this paper we show that every g-frame for an \linebreak infinite dimensional Hilbert space $\mathcal{H}$ can be written as a sum of three g-orthonormal bases for $\mathcal{H}$. Also, we prove that every g-frame can be represented as a…

We consider pairs of operators $A,B\in B(H)$, where $H$ is a Hilbert space, such that there exist a linear isometry $f$ from the span of $\{A,B\}$ into $\mathbb{C}^2$ mapping $A,B$ into orthonormal vectors. We prove some necessary…

Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation relation of quantum theory and discuss a…

In this letter we present a general classification of integrable models of identical classical spins coupled via the isotropic Heisenberg Hamiltonian. Our constructive proof of integrability provides a solution scheme for the equations…

A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift…