Related papers: Gurarii operators are generic

The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA/0612798. We prove that generically their action on…

A sequence in a $C^*$-algebra $A$ is called completely Sidon if its span in $A$ is completely isomorphic to the operator space version of the space $\ell_1$ (i.e. $\ell_1$ equipped with its maximal operator space structure). The latter can…

In a recent paper, we introduced and studied the class of admissible noncommutative domains $D_{g^{-1}}(H)$ in $B(H)^n$ associated with admissible free holomorphic functions $g$ in noncommutative indeterminates $Z_1,\ldots, Z_n$. Each such…

In this note we study algebras of chiral differential operators over an algebraic group and over homogeneous spaces $G/G'$ where $G$ is simple and $G'$ is unipotent or parabolic.

We prove a differential analogue of Hilbert's irreducibility theorem. Let $\mathcal{L}$ be a linear differential operator with coefficients in $C(\mathbb{X})(x)$ that is irreducible over $\overline{C(\mathbb{X})}(x)$, where $\mathbb{X}$ is…

This is the second of two papers treating faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties; in the first paper we considered the module itself and its projective space, while…

Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was…

For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…

We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…

A generic computation of a subset $A$ of $\mathbb{N}$ is a computation which correctly computes most of the bits of $A$, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory,…

Using Read's construction of operators without non-trivial invariant subspaces/subsets on $\ell_{1}$ or $c_{0}$, we construct examples of operators on a Hilbert space whose set of hypercyclic vectors is "large" in various senses. We give an…

In this paper, we characterize the dynamic of every abelian subgroups $\mathcal{G}$ of GL($n$, $\mathbb{K}$), $\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$. We show that there exists a $\mathcal{G}$-invariant, dense open set $U$ in…

The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…

The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…

We define a strong Morita-type equivalence $\sim _{\sigma \Delta }$ for operator algebras. We prove that $A\sim _{\sigma \Delta }B$ if and only if $A$ and $B$ are stably isomorphic. We also define a relation $\subset _{\sigma \Delta }$ for…

It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…

We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the $\phi^4$ theory where the parameters of the theory are…

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…

Higher form symmetry, one of the generalized symmetries, primarily involves the action of abelian groups. This is, due to the topological nature of symmetry defect operators. In this study, we extend the vector space (or vector bundle) in…

Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p \geqslant 0$ which is not algebraic over a finite field. Let $\mathcal{C}_1, \ldots, \mathcal{C}_t$ be non-central conjugacy…