2005/12/05 by Jun Hu, Hu, Jun
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.CO #math.RT
paper · pdf · doi:10.48550/arxiv.math/0512111
openalex publication_date 2005/12/05 · arxiv created 2006/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 A2ℓ(2) and of type Dℓ+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.