相关论文: Commutativity of missing label operators in terms …
We analyze under which conditions the missing label problem associated to a reduction chain $\frak{s}^{\prime}\subset \frak{s}$ of (simple) Lie algebras can be completely solved by means of an In\"on\"u-Wigner contraction $\frak{g}$…
We show that the In\"on\"u-Wigner contraction naturally associated to a reduction chain $\frak{s}\supset \frak{s}^{\prime}$ of semisimple Lie algebras induces a decomposition of the Casimir operators into homogeneous polynomials, the terms…
We briefly review a matrix based method to compute the Casimir operators of Lie algebras, mainly certain type of contractions of simple Lie algebras. The versatility of the method is illustrated by constructing matrices whose characteristic…
In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…
This paper is an attempt to unify the multivariable operator model theory for ball-like domains and commutative polydiscs, and extend it to a more general class of noncommutative polydomains. An important role in our study is played by…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
The goal of this paper is to prove operator identities using equalities between noncommutative polynomials. In general, a polynomial expression is not valid in terms of operators, since it may not be compatible with domains and codomains of…
We obtain a family of polynomials defined by vanishing conditions and associated to tangles. We study more specifically the case where they are related to a O(n) loop model. We conjecture that their specializations at $z_i=1$ are {\it…
We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient condition is based on an analysis…
Many relevant applications of group theoretical methods to physical problems are related, in some manner, to classification schemes by means of symmetry groups. In these schemes, irreducible representations of a Lie group have to be…
Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial…
In this paper we prove that the classical Lie bracket of vector fields can be generalized to the noncommutative setting by antisymmetrizing (in a suitable noncommutative sense) their compositions. This construction turns out to depend on…
In this paper, we study noncommutative varieties in polydomains in $B(H)^n$. The goal is to understand the structure of these varieties, determine their elements and classify them up to unitary equivalence. Using noncommutative Berezin…
We initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space, which is generated by certain positivity conditions on polynomials in n noncommutative indeterminates. We obtain Fatou…
In this paper we present a general framework for Berezin covariant symbols, and we discuss a few basic properties of the corresponding symbol map, with emphasis on its injectivity in connection with some problems in representation theory of…
We investigate the real Lie algebra of first-order differential operators with polynomial coefficients, which is subject to the following requirements. (1) The Lie algebra should admit a basis of differential operators with homogeneous…
In this article, we completely characterize the Berezin range of Toeplitz operators with harmonic symbols acting on weighted Bergman spaces, illustrating the necessity of the harmonicity condition through examples. We then introduce a new…
We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…
We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant…
The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalisable set of Casimir operators in the subgroup chain GL(3)…