Mullineux involution and twisted affine Lie algebras

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dc.creatorHu, Jun
dc.date2005-12-05
dc.date2006-04-02
dc.date.accessioned2026-07-07T06:54:53Z
dc.date.available2026-07-07T06:54:53Z
dc.descriptionWe use Naito-Sagaki's work [S. Naito & D. Sagaki, J. Algebra 245 (2001) 395--412, J. Algebra 251 (2002) 461--474] on Lakshmibai-Seshadri paths fixed by diagram automorphisms to study the partitions fixed by Mullineux involution. We characterize the set of Mullineux-fixed partitions in terms of crystal graphs of basic representations of twisted affine Lie algebras of type $A_{2\ell}^{(2)}$ and of type $D_{\ell+1}^{(2)}$. We set up bijections between the set of symmetric partitions and the set of partitions into distinct parts. We propose a notion of double restricted strict partitions. Bijections between the set of restricted strict partitions (resp., the set of double restricted strict partitions) and the set of Mullineux-fixed partitions in the odd case (resp., in the even case) are obtained.
dc.identifierhttps://arxiv.org/abs/math/0512111
dc.identifierhttp://arxiv.org/abs/math/0512111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106099
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.titleMullineux involution and twisted affine Lie algebras
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