相关论文: Hessenberg Input Normal Representations
The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $\mathbb{H}^2$. We introduce a conformal version of the Laplacian and we prove that the distance…
A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if G is an abelian group, then the follwing are equivalent: 1. Th(G, +) has the…
Two $n$-dimensional vectors $A$ and $B$, $A,B \in \mathbb{R}^n$, are said to be \emph{trivially orthogonal} if in every coordinate $i \in [n]$, at least one of $A(i)$ or $B(i)$ is zero. Given the $n$-dimensional Hamming cube $\{0,1\}^n$, we…
We prove that any product of two non-abelian free groups, $\Gamma=\mathbb F_m\times\mathbb F_k$, for $m,k\geq 2$, is not Hilbert-Schmidt stable. This means that there exist asymptotic representations $\pi_n:\Gamma\rightarrow…
The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator $X$ and a nondecreasing function $h$. The family of Hessenberg varieties for regular $X$ is particularly important: they are used in quantum…
A regular nilpotent Hessenberg Schubert cell is the intersection of a regular nilpotent Hessenberg variety with a Schubert cell. In this paper, we describe a set of minimal generators of the defining ideal of a regular nilpotent Hessenberg…
Let G be a reductive group over a non-archimedean local field F. Consider an arbitrary Bernstein block Rep(G)^s in the category of complex smooth G-representations. In earlier work the author showed that there exists an affine Hecke algebra…
Dynamics of a quantum system can be described by coupled Heisenberg equations. In a generic many-body system these equations form an exponentially large hierarchy that is intractable without approximations. In contrast, in an integrable…
In this paper we give a Casimir Invariant for the Symmetric group $S_n$. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of…
In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time,…
We prove that metabelian Baumslag$-$Solitar group $BS(1,k)$, $k>1$, is (strongly) regularly bi-interpretable with the ring of integers $\mathbb{Z}$, and describe in algebraic terms all groups that are elementarily equivalent to $BS(1,k)$.
The original Bondi$-$Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian 4-dim space$-$times. As such, B is the best candidate for the universal symmetry group of General Relativity…
For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable.…
We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…
Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of…
We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of…
Let $G$ be a connected semisimple Lie group with a finite center, with a maximal compact subgroup $K$. There are two general methods to construct representations of $G$, namely, ordinary parabolic induction and cohomological parabolic…
We give an asymptotic formula for the mean value of the number of representations of an integer as sum of two squares known as the Gauss circle problem.