Related papers: Iterated function systems and permutation represen…

We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz…

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…

Let ${\rm Rep}\,{\cal O}_n$ denote the category of all nondegenerate $^*$ representations of the Cuntz algebra ${\cal O}_n$. For any $2\leq n,m<\infty$, we construct an isomorphism functor $F_{n,m}$ from ${\rm Rep}\,{\cal O}_m$ to ${\rm…

We study representations of the central extension of the Lie algebra of differential operators on the circle, the W-infinity algebra. We obtain complete and specialized character formulas for a large class of representations, which we call…

We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…

The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical…

A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…

Infinite dimensional representations of the real form U_q(u_{n,1}) of the Drinfeld--Jimbo algebra U_q(gl_{n+1}) are defined. The principal series of representations of U_q(u_{n,1}) is studied. Intertwining operators for pairs of the…

The conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n) give rise to a one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra…

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…

We consider representations of Cuntz--Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron-Frobenius…

Unital endomorphisms of the Cuntz algebra O_n which preserve the canonical UHF-subalgebra F_n of O_n are investigated. We give examples of such endomorphisms for which the associated unitary element in O_n does not belong to F_n. One such…

We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…

Highest weight representations of $U_q(su(1,1))$ with $q=\exp \pi i/N$ are investigated. The structures of the irreducible hieghesat weight modules are discussed in detail. The Clebsch-Gordan decomposition for the tensor product of two…

We establish new restrictions on the values of the lifting obstruction for projective unitary representations of second countable, locally compact Hausdorff groups on operator algebras. Using these, we show that every projective…

We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized…

Let $R$ be a root datum with affine Weyl group $W^e$, and let $H = H (R,q)$ be an affine Hecke algebra with positive, possibly unequal, parameters $q$. Then $H$ is a deformation of the group algebra $\mathbb C [W^e]$, so it is natural to…

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of…

In arXiv:2503.19532 new examples of ribbon Hopf algebras based on the construction due to Nenciu were presented. This piece serves as a sequel where we study the representation theory of these new examples of ribbon Hopf algebras. We…

We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…