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We study the little groups of the minima of the Higgs potential built on the representation 75 of SU(5). We find a minimum with a non maximal little subalgebra, but an additional discrete group so that the little group is maximal. We find a large class of minimas with su(3) + su(2) + u(1) little algebra.
Generalizing a procedure of Gomez and Sierra, we realize simple quantum groups by their action on screened vertex operators of WZNW models in the Coulomb gas representation.
The algebra SU(2)q is realized by q-differential operators on polynomials in two variables. The method of van der Waerden for computing SU(2) C.G. coefficients is generalized to SU(2)q.
We consider the Hamiltonian and Lagrangian formalism describing free κ-relativistic particles with their four-momenta constrained to the κ-deformed mass shell. We study the formalism with commuting as well as noncommuting (i.e., with nonvanishing Poisson brackets) space-time coordinates; in particular a κ-deformed phase space formalism leading to the κ-deformed covariant Heisenberg algebra is presented...
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