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arXiv · 2301.00941

A new approach to the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups

Zachary Carlini
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Abstract

We give a new, conceptual proof of the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups. The key to our approach is a new formula for the comultiplication of the $\imath$-divided powers, which allows us to reformulate the relations in terms of the adjoint action. We then obtain a proof using properties of the adjoint representation. The flexibility of this approach allows us to establish a more general family of relations which seem difficult to establish otherwise.

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BibTeXRIS

Zachary Carlini. 2023-01-03. A new approach to the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups. https://arxiv.org/abs/2301.00941

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