Intertwiner for Quantized Coordinate Ring $$A_q(G_2)$$

Atsuo Kuniba

doi:10.1007/978-981-19-3262-5_8

Intertwiner for Quantized Coordinate Ring $$A_q(G_2)$$

Atsuo Kuniba

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https://doi.org/10.1007/978-981-19-3262-5_8

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Publication Date: Jan 1, 2022

Affiliation: The University of Tokyo

#Reflection Equation #Fundamental Representations + Show 8 more

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Abstract

AbstractThe quantized coordinate ring $A_q(G_2)$ is formulated in terms of generators and relations. Fundamental representations are presented explicitly. Basic properties of the intertwiner associated with the order six Coxeter relation are derived. Since there is no “$G_3$”, we do not have a compatibility condition analogous to the tetrahedron or 3D reflection equations. Nevertheless, the intertwining relation still admits a reformulation as what we call the quantized $G_2$ reflection equation. This fact will be utilized to construct matrix product solutions to the $G_2$ reflection equation in Chap. 17.

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