Č. Burdík

ON THE MIXED SYMMETRY IRREDUCIBLE REPRESENTATIONS OF THE POINCARÉ GROUP IN THE BRST APPROACH

The Lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is adopted to the systems of second-class constraints by the construction of an auxiliary representations of the algebras of constraints in terms of Verma modules.

The lagrangian description of representations of the Poincare group

Abstract The construction of lagrangians describing the various representations of the Poincare group is given in terms of the BRST approach.

On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s1,..., sk) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s1, s2) is derived.

N = 4 supersymmetric Eguchi−Hanson sigma model in d =1 ∗ )

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi-Hanson target space is investigated in detail: we present the standard and quotient approaches to get the Eguchi-Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric.

Complete branching rules generating function for SO(7) contains/implies SU(2)3 and polynomial basis states

A branching rules generating function is given for SO(7) contains/implies SU(2)3, along with its interpretation in terms of basis states, and instructions for calculating generator matrix elements. The generator matrix elements for the degenerate (0,0,c) representations are calculated as an example of this procedure.

Wavelet multiresolutions for the Fibonacci chain

Most of the discrete wavelet families are periodic dyadic: they live on the multiresolution sequence { /2j }j of lattice backgrounds at different scales. We present here a construction of wavelet family based on a sequence of aperiodic discretizations of . At a given scale, this discretization is the point set of nodes of the Fibonacci chain, a well known stone-inflation cut and project model for one-dimensional quasicrystals. Corresponding multiresolution analysis and the elementary example of the Haar system are presented.

Standard complex for quantum Lie algebras

For a quantum Lie algebra Γ, let Γ^ be its exterior extension (the algebra Γ^ is canonically defined). We introduce a differential on the exterior extension algebra Γ^ which provides the structure of a complex on Γ^. In the situation when Γ is a usual Lie algebra, this complex coincides with the “standard complex.” The differential is realized as a commutator with a (BRST) operator Q in a larger algebra Γ^[Ω], with extra generators canonically conjugated to the exterior generators of Γ^. A recurrent relation which uniquely defines the operator Q is given.

BETA-INTEGERS AS A GROUP

Discrete sets of numbers related to some irrational number , called the-integers Z , are a natural tool to describe quasicrystals. We prove that, when is a quadratic Pisot unit, the set Z is a group isomorphic to the set of integers Z.

The universal R-matrix and the Yang-Baxter equation with parameters

The authors formulate, and demonstrate with some examples, a method for obtaining solutions of the Yang-Baxter equation with parameters.

A Two parametric quantization of sl(2)

A two-parametric solution of the constant Yang-Baxter equation is used for the construction of structures corresponding to quantized groups. The corresponding Hopf algebra is generated by five generators.