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Mariano A. del Olmo

Publications and source records attributed to Mariano A. del Olmo.

22 records · Page 2Linked to original sources
arXiv1999

Extended and Reshetikhin Twists for sl(3)

The properties of the set {L} of extended jordanian twists for algebra sl(3) are studied. Starting from the simplest algebraic construction --- the peripheric Hopf algebra U_ P'(0,1)(sl(3)) --- we construct explicitly the complete family of extended twisted algebras {U_ E(θ)(sl(3))} corresponding to the set of 4-dimensional Frobenius subalgebras {L(θ)} in sl(3). It is proved that the extended twisted algebras with different values of the parameter θare connected by a special kind of Reshetikhin twist. We study the relations between the family {U_E(θ)(sl(3))} and the one-dimensional set {U_DJR(λ)(sl(3))} produced by the standard Reshetikhin twist from the Drinfeld--Jimbo quantization U_DJ(sl(3)). These sets of deformations are in one-to-one correspondence: each element of {U_E(θ)(sl(3))} can be obtained by a limiting procedure from the unique point in the set {U_DJR(λ)(sl(3))}.

math.QA↗
arXiv1998

Peripheric Extended Twists

The properties of the set L of extended jordanian twists are studied. It is shown that the boundaries of L contain twists whose characteristics differ considerably from those of internal points. The extension multipliers of these "peripheric" twists are factorizable. This leads to simplifications in the twisted algebra relations and helps to find the explicit form for coproducts. The peripheric twisted algebra U(sl(4)) is obtained to illustrate the construction. It is shown that the corresponding deformation U_{P}(sl(4)) cannot be connected with the Drinfeld--Jimbo one by a smooth limit procedure. All the carrier algebras for the extended and the peripheric extended twists are proved to be Frobenius.

math.QA↗
arXiv1998

Coherent states on the circle

A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bièvre and González in [DG 92], is carried out. They were obtained from the Weyl-Heisenberg coherent states in $L^2(\R)$ by means of the Weil-Brezin-Zak transformation, they are labeled by the points of the cylinder $S^1 \times \R$, and they provide a realization of $L^2(S^1)$ by entire functions (similar to the well-known Fock-Bargmann construction). In particular, we compute the expectation values of the position and momentum operators on the circle and we discuss the Heisenberg uncertainty relation.

quant-ph↗