On the tensor product of two basic representations of $U_v(\hat{sl}_e)$

dc.creatorAriki, Susumu
dc.creatorKreiman, Victor
dc.creatorTsuchioka, Shunsuke
dc.date2006-06-02
dc.date2007-12-20
dc.date.accessioned2026-07-07T08:50:26Z
dc.date.available2026-07-07T08:50:26Z
dc.descriptionLet $\{B(Λ_m)|m\in\Z/e\Z\}$ be the set of level one $\mathfrak{g}(A^{(1)}_{e-1})$-crystals, and consider the realization of $B(Λ_m)$ using $e$-restricted partitions. We prove a purely Young diagrammatic criterion for an element of $B(Λ_0)^{\otimes d_1}\otimes B(Λ_m)^{\otimes d_2}$ to be in the component $B(d_1Λ_0+d_2Λ_m)$. As an application, we give a non-recursive characterization of simple modules of the Hecke algebra of type $B$. In the course of the proof, we also obtain a combinatorial description of the second type of Kashiwara's Demazure crystal in $B(Λ_m)$.
dc.description52 pages, (v2,v3) typos and reference numbers corrected, (v4,v5) minor revision
dc.identifierhttps://arxiv.org/abs/math/0606044
dc.identifierhttp://arxiv.org/abs/math/0606044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144606
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleOn the tensor product of two basic representations of $U_v(\hat{sl}_e)$
dc.typetext

Files

Collections