Related papers: A realization of the quantum Lorentz group
In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation…
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…
We present the q-deformed counterpart of the local representations of the (1+1) extended Galilei group. These representations act on the space of wavefunctions defined in the space-time. As in the classical case the q-local representations…
To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
The positive-energy unitary irreducible representations of the $q$-deformed conformal algebra ${\cal C}_q = {\cal U}_q(su(2,2))$ are obtained by appropriate deformation of the classical ones. When the deformation parameter $q$ is $N$-th…
We prove that if $G$ is a finite simple group, then all irreducible complex representations of $G$ by be realized over the real numbers if and only if every element of $G$ may be written as a product of two involutions in $G$. This follows…
A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for…
Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.
A class of representations is described for the central extensions, found by Etingof and Frenkel, of current algebras over Riemann surfaces. Their irreducibility is proved. The possibility/impossibility to obtain integrable representations…
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
We consider one dimensional deformed Heisenberg algebra leading to existence of minimal length for coordinate operator and minimal and maximal uncertainty of momentum operator. For this algebra an exactly solvable Hamiltonian is…
We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide with the Drinfeld-Jimbo quantum algebra U_q(so(n)) of the…
We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for…
We prove that the Steinberg representation of a connected reductive group over an infinite field is irreducible. For finite fields, this is a classical theorem of Steinberg and Curtis.
We introduce the Pythagorean dimension: a natural number (or infinity) for all representations of the Cuntz algebra and certain unitary representations of the Richard Thompson groups called Pythagorean. For each natural number d we…
In this paper we prove that every irreducible representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition. We also prove that - in general - for (semi)simple…
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…