Related papers: Wigner-Eckart theorem for the non-compact algebra …
We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a…
This letter continues the program aimed at analysis of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU(2). The formal scalar product is expressed as a multiple finite dimensional integral…
Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space and the set of representing or Jensen measures for this cone. In this paper we prove non-compact versions of this theorem.
In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We…
An n-particle 3-dimensional Wigner quantum oscillator model is constructed explicitly. It is non-canonical in that the usual coordinate and linear momentum commutation relations are abandoned in favour of Wigner's suggestion that Hamilton's…
We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a…
The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short)…
In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a…
We construct the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over compact discrete valuation rings of even residual characteristic. We also prove that the complex group algebras of $\mathrm{SL}_2$ over finite…
We construct classes of von Neumann algebra modules by considering ``column sums" of noncommutative L^p spaces. Our abstract characterization is based on an L^{p/2}-valued inner product, thereby generalizing Hilbert C*-modules and…
We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a…
After explaining the concepts of Langlands dual and miniscule representations, we define an analog of the Gauss sum for any compact, simple Lie group with a simply laced Lie algebra. We then show a reciprocity property when a Lie group is…
While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge…
This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable ${\cal Z}$-absorbing C*-algebras with locally finite decomposition property satisfying the UCT whose…
We first discuss the relationship between the SL(2;R)/U(1) supercoset and N=2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;R)/U(1) theory…
Noether's Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws.…
It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special…
We represent a general bilinear Calder\'on-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse T1…
Given a contractive tuple of Hilbert space operators satisfying certain $A$-relations we show that there exists a unique minimal dilation to generators of Cuntz-Krieger algebras or its extension by compact operators. This Cuntz-Krieger…
The so called Gell-Mann formula expresses the Lie algebra elements in terms of the corresponding Inonu-Wigner contracted ones. In the case of sl(n, R) and su(n) algebras contracted w.r.t. so(n) subalgebras, the Gell-Mann formula is…