Freidel-Maillet type presentations of $U_q(sl_2)$

Abstract : A unified framework for the Chevalley and equitable presentation of $U_q(sl_2)$ is introduced. It is given in terms of a system of Freidel-Maillet type equations satisfied by a pair of quantum K-operators ${\cal K}^\pm$, whose entries are expressed in terms of either Chevalley or equitable generators. The Hopf algebra structure is reconsidered in light of this presentation, and interwining relations for K-operators are obtained. A K-operator solving a spectral parameter dependent Freidel-Maillet equation is also considered. Specializations to $U_q(sl_2)$ admit a decomposition in terms of ${\cal K}^\pm$. Explicit examples of K-matrices are constructed.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03279107
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Submitted on : Tuesday, July 6, 2021 - 11:35:24 AM
Last modification on : Wednesday, July 7, 2021 - 3:27:56 AM

Citation

Pascal Baseilhac. Freidel-Maillet type presentations of $U_q(sl_2)$. 2021. ⟨hal-03279107⟩

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