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Mullineux involution and twisted affine Lie algebras
We 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
and of type . 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
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