General Construction of Nonstandard $R_h$-matrices as Contraction Limits of $R_{q}$-matrices

B. Abdesselam; A. Chakrabarti; R. Chakrabarti

doi:10.1142/S021773239800084X

paper

General Construction of Nonstandard $R_{h}$ -matrices as Contraction Limits of $R_{q}$ -matrices

arXiv:q-alg/9706033 · doi:10.1142/S021773239800084X

Abstract

A class of transformations of $R_{q}$ -matrices is introduced such that the $q \to 1$ limit gives explicit nonstandard $R_{h}$ -matrices. The transformation matrix is singular itself at $q \to 1$ limit. For the transformed matrix, the singularities, however, cancel yielding a well-defined construction. Our method can be implemented systematically for R-matrices of all dimensions and not only for $s l (2)$ but also for algebras of higher dimensions. Explicit constructions are presented starting with $U_{q} (s l (2))$ and $U_{q} (s l (3))$ , while choosing $R_{q}$ for (fund. rep.) $\otimes$ (arbitrary irrep.). The treatment for the general case and various perspectives are indicated. Our method yields nonstandard deformations along with a nonlinear map of the $h$ -Borel subalgebra on the corresponding classical Borel subalgebra. For $U_{h} (s l (2))$ this map is extended to the whole algebra and compared with another one proposed by us previously.

11 pages, no figures

General Construction of Nonstandard Rh​-matrices as Contraction Limits of Rq​-matrices

Abstract

Cited by in corpus (13)

General Construction of Nonstandard $R_{h}$ -matrices as Contraction Limits of $R_{q}$ -matrices