2011/12/16 by Motohiro Ishii, Ishii, Motohiro
Mathematics · #17B10 (Secondary) #81R10 (Primary) 05E10 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CO #math.QA #math.RT #msc:05E10 #msc:17B10 #msc:81R10
paper · pdf · doi:10.48550/arxiv.1112.3708
30 pages
openalex publication_date 2011/12/16 · arxiv created 2013/04/14 · arxiv updated 2013/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that Joseph-Lamprou's path model for representations of generalized Kac-Moody algebras can be embedded into Littelmann's path model for certain Kac-Moody algebras. Using this embedding, for Joseph-Lamprou's path crystals, we give a decomposition rule for tensor product and a branching rule for restriction to Levi subalgebras. Also, we obtain a characterization of standard paths in terms of a certain monoid, which can be thought of as a generalization of a Coxeter group.