Quantum Symmetric Pairs and the Reflection Equation

Details Quantum Symmetric Pairs and the Reflection Equation Quantum Symmetric Pairs and the Reflection Equation

2005-12-27

arxiv.org/abs/math/0512581v2

Mathematics

Quantum Algebra

largely extended version, LaTex2e, 33 pages

Scientific paper

It is shown that central elements in G. Letzter's quantum group analogs of symmetric pairs lead to solutions of the reflection equation. This clarifies the relation between Letzter's approach to quantum symmetric pairs and the approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen. We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type construction of quantum symmetric pairs can be performed preserving spherical representations from the classical situation. These tools apply to the symmetric pair FII and to all symmetric pairs which correspond to an automorphism of the underlying Dynkin diagram. Hence Noumi-Sugitani-Dijkhuizen type constructions with desirable properties are possible for various symmetric pairs for exceptional Lie algebras.

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