Related papers: Why the Mickelsson-Faddeev algebra lacks unitary r…
In this paper, the Moyal star-product quantization is used to construct the unitary irreducible representations of the Euclidean motion group on 3-dimensions. These unitary representations will come from the representation of its Lie…
The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
One proves the uniqueness of distributional solutions to nonlinear Fokker--Planck equations with monotone diffusion term and derive as a consequence (restricted) uniqueness in law for the corresponding McKean--Vlasov stochastic differential…
Let $C$ and $A$ be two unital separable amenable simple C*-algebras with tracial rank no more than one. Suppose that $C$ satisfies the Universal Coefficient Theorem and suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We…
Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called accessibility - is the starting point of…
By Glimm's dichotomy, a separable, simple $\textrm{C}^*$-algebra has continuum-many unitarily inequivalent irreducible representations if, and only if, it is non-type I while all of its irreducible representations are unitarily equivalent…
The product of two unitaries can normally be expressed as a single exponential through the famous Baker-Campbell-Hausdorff formula. We present here a counterexample in quantum optics, by showing that an expression in terms of a single…
We show that every infinite-dimensional commutative unital C*-algebra has a Hilbert C*-module admitting no frames. In particular, this shows that Kasparov's stabilization theorem for countably generated Hilbert C*-modules can not be…
We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group $\mathfrak{S}_n$ over the complex numbers. Interestingly, the…
C*-algebras are rings, sometimes nonunital, obeying certain axioms that ensure a very well-behaved representation theory upon Hilbert space. Moreover, there are some well-known features of the representation theory leading to subtle…
We present a new look at description of real finite-dimensional Lie algebras. The basic element turns out to be a pair $(F,v)$ consisting of a linear mapping $F\in End(V)$ and its eigenvector $v$. This pair allows to build a Lie bracket on…
We study non-selfadjoint representations of a finite dimensional real Lie algebra $\fg$. To this end we embed a non-selfadjoint representation of $\fg$ into a more complicated structure, that we call a $\fg$-operator vessel and that is…
E(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the group are realized is explicitely constructed. The addition…
We construct a C*-algebra that has only one irreducible representation up to unitary equivalence but is not isomorphic to the algebra of compact operators on any Hilbert space. This answers an old question of Naimark. Our construction uses…
We consider integrable, category O-modules of indecomposable symmetrizable Kac-Moody algebras. We prove that unique factorization of tensor products of irreducible modules holds in this category, upto twisting by one dimensional modules.…
In gauge theory, the Faddeev-Mickelsson-Shatashvili anomaly arises as a prolongation problem for the action of the gauge group on a bundle of projective Fock spaces. In this paper, we study this anomaly from the point of view of bundle…
Let $F$ be a $p$-adic field, and $K$ a quadratic extension of $F$. Using Tadic's classification of the unitary dual of $GL(n,K)$, we give the list of irreducible unitary representations of this group distinguished by $GL(n,F)$, in terms of…
We attempt to reconstruct the irreducible unitary representations of the Banach Lie group $U_0(\H)$ of all unitary operators $U$ on a separable Hilbert space $\H$ for which $U-{\mathbb I}$ is compact, originally found by Kirillov and…
We establish completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable if and only if its embedding into minimal logic, mFOL, is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the…