The augmented tridiagonal algebra

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dc.creatorIto, Tatsuro
dc.creatorTerwilliger, Paul
dc.date2009-04-20
dc.date.accessioned2026-07-07T13:05:50Z
dc.date.available2026-07-07T13:05:50Z
dc.descriptionMotivated by investigations of the tridiagonal pairs of linear transformations, we introduce the augmented tridiagonal algebra ${\mathcal T}_q$. This is an infinite-dimensional associative ${\mathbb C}$-algebra with 1. We classify the finite-dimensional irreducible representations of ${\mathcal T}_q$. All such representations are explicitly constructed via embeddings of ${\mathcal T}_q$ into the $U_q(sl_2)$-loop algebra. As an application, tridiagonal pairs over ${\mathbb C}$ are classified in the case where $q$ is not a root of unity.
dc.description67 pages
dc.identifierhttps://arxiv.org/abs/0904.2889
dc.identifierhttp://arxiv.org/abs/0904.2889
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227621
dc.subjectQuantum Algebra
dc.subjectCombinatorics
dc.subject17B37, 05E30
dc.titleThe augmented tridiagonal algebra
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