Related papers: Resolvent algebra in Fock-Bargmann representation
We introduce coordinates on the spaces of framed and decorated representations of the fundamental group of a surface with nonempty boundary into the symplectic group $Sp(2n,\mathbf R)$. These coordinates provide a noncommutative…
The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement A in C^n; it is the quotient of an exterior algebra E(V) on |A| generators. Orlik and Terao introduced a commutative analog S(V)/I of the…
For any Hermitian Lie group $G$ of tube type we give a geometric quantization procedure of certain $K_{\mathbb{C}}$-orbits in $\mathfrak{p}_{\mathbb{C}}^*$ to obtain all scalar type highest weight representations. Here $K_{\mathbb{C}}$ is…
Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let $\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$ generated by all…
We consider symmetric separately radial (with corresponding group $S_n\rtimes \mathbb{T}^n$) and alternating separately radial (with corresponding group $A_n\rtimes \mathbb{T}^n$) symbols, as well as the associated Toeplitz operators on the…
A commutative Rota-Baxter algebra can be regarded as a commutative algebra that carries an abstraction of the integral operator. With the motivation of generalizing the study of algebraic geometry to Rota-Baxter algebra, we extend the…
We extend the notion of Rokhlin dimension from topological dynamical systems to $C^*$-correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiagonal-like condition (which, for example, is automatic for…
Given a semisimple compact Lie group $G$ and a nonzero dominant integral weight $\lambda$, the highest weight $G_q$-modules $V_{n\lambda}$ form a subproduct system of finite dimensional Hilbert spaces. Using a conjectural asymptotic…
Let $\sigma$ be the involution of the Roe algebra $\Roe{\RR}$ which is induced from the reflection $\RR\to\RR; x\mapsto -x$. A graded Fredholm module over a separable $C^*$-algebra $A$ gives rise to a homomorphism…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
For any given bounded symmetric domain, we prove the existence of commutative $C^*$-algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of the Toeplitz operators that generate such algebras are defined…
We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably…
Let G be a reductive p-adic group and let H(G)^s be a Bernstein block of the Hecke algebra of G. We consider two important topological completions of H(G)^s: a direct summand S(G)^s of the Harish-Chandra--Schwartz algebra of G and a…
To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2…
A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is the complete characterization of the set of all Toeplitz operators that commute with a given operator. In \cite{al}, the…
It is shown that topological freeness of Rieffel's induced representation functor implies that any $C^*$-algebra generated by a faithful covariant representation of a Hilbert bimodule $X$ over a $C^*$-algebra $A$ is canonically isomorphic…
Recently, relative Rota-Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider relative Rota-Baxter Leibniz algebras (rRB Leibniz algebras) as the object of…
We present a representation of skew-orthogonal polynomials of symplectic type ($\beta=4$) in terms of a matrix Riemann-Hilbert problem, for weights of the form ${\rm e}^{-V(z)}$ where $V$ is a polynomial of even degree and positive leading…
This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…