Reflection equation for the N=3 Cremmer-Gervais R-matrix

Abstract

We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The reflection equation is shown to be equivalent to 38 equations which do not depend on the parameter of the R-matrix, q. Solving those 38 equations. the solution space is found to be the union of two types of spaces, each of which is parametrized by the algebraic variety ${\mathbb{P}}^1(\mathbb{C})\times {\mathbb{P}}^1(\mathbb{C})\times {\mathbb{P}}^2(\mathbb{C})$ and $\mathbb{C}\times {\mathbb{P}}^1(\mathbb{C})\times {\mathbb{P}}^2(\mathbb{C})$.

28 pages, revised version

Cited by in corpus (1)

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