Higher order relations for ADE-type generalized q-Onsager algebras

Abstract

Let $\{A_j|j=0,1,...,rank(g)\}$ be the fundamental generators of the generalized $q-$Onsager algebra ${\mathcal{O}}_q(\hat{g})$ introduced in \cite{BB1}, where $\hat{g}$ is a simply-laced affine Lie algebra. New relations between certain monomials of the fundamental generators - indexed by the integer $r\in {\mathbb{Z}}^{+}$ - are conjectured. These relations can be seen as deformed analogues of Lusztig's $r-$th higher order $q-$Serre relations associated with ${\mathcal{U}}_q(\hat{g})$, which are recovered as special cases. The relations are proven for $r\le 5$. For $r$ generic, several supporting evidences are presented.

9 pages; Presentation improved

Cited by in corpus (2)

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