Irreducible Modules for the Quantum Affine Algebra $U_q(\hat{sl}_2)$ and its Borel subalgebra $U_q(\hat{sl}_2)^{\geq 0}$

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dc.creatorBenkart, Georgia
dc.creatorTerwilliger, Paul
dc.date2003-11-10
dc.date.accessioned2026-07-07T05:02:46Z
dc.date.available2026-07-07T05:02:46Z
dc.descriptionLet $U_q(\hat{sl}_2)^{\geq 0}$ denote the Borel subalgebra of the quantum affine algebra $U_q(\hat{sl}_2)$. We show that the following hold for any choice of scalars $ε_0, ε_1$ from the set ${1,-1}$. (i) Let $V$ be a finite-dimensional irreducible $U_q(\hat{sl}_2)^{\geq 0}$-module of type $(ε_0,ε_1)$. Then the action of $U_q(\hat{sl}_2)^{\geq 0}$ on $V$ extends uniquely to an action of $U_q(\hat{sl}_2)$ on $V$. The resulting $U_q(\hat{sl}_2)$-module structure on $V$ is irreducible and of type $(ε_0,ε_1)$. (ii) Let $V$ be a finite-dimensional irreducible $U_q(\hat{sl}_2)$-module of type $(ε_0,ε_1)$. When the $U_q(\hat{sl}_2)$-action is restricted to $U_q(\hat{sl}_2)^{\geq 0}$, the resulting $U_q(\hat{sl}_2)^{\geq 0}$-module structure on $V$ is irreducible and of type $(ε_0,ε_1)$.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0311152
dc.identifierhttp://arxiv.org/abs/math/0311152
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69140
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleIrreducible Modules for the Quantum Affine Algebra $U_q(\hat{sl}_2)$ and its Borel subalgebra $U_q(\hat{sl}_2)^{\geq 0}$
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