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Generalized Onsager algebras. (arXiv:1810.07408v1 [math.RT])
来源于:arXiv
Let $\mathfrak{g}(A)$ be the Kac-Moody algebra with respect to a
symmetrizable generalized Cartan matrix $A$. We give an explicit presentation
of the fix-point Lie subalgebra $\mathfrak{k}(A)$ of $\mathfrak{g}(A)$ with
respect to the Chevalley involution. It is a presentation of $\mathfrak{k}(A)$
involving inhomogeneous versions of the Serre relations, or, from a different
perspective, a presentation generalizing the Dolan-Grady presentation of the
Onsager algebra. In the finite and untwisted affine case we explicitly compute
the structure constants of $\mathfrak{k}(A)$ in terms of a Chevalley type basis
of $\mathfrak{k}(A)$. For the symplectic Lie algebra and its untwisted affine
extension we explicitly describe the one-dimensional representations of
$\mathfrak{k}(A)$. 查看全文>>