2012/01/21 by Ivan Losev, Losev, Ivan · 1 citation
Chemistry · Mathematics · #05E10 (Primary) 16G99 #17B10 #18D99 #20G05 (Secondary) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Combinatorics (math.CO) #Crystallography and molecular interactions #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT) #math.CO #math.CT #math.RT #msc:05E10 #msc:16G99 #msc:17B10 #msc:18D99 #msc:20G05
paper · pdf · doi:10.48550/arxiv.1201.4493
15 pages; v2 minor changes
openalex publication_date 2012/01/21 · arxiv created 2012/02/12 · arxiv updated 2012/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define highest weight categorical actions of sl2 on highest weight categories and show that basically all known examples of categorical sl2-actions on highest weight categories (including rational and polynomial representations of general linear groups, parabolic categories O of type A, categories O for cyclotomic Rational Cherednik algebras) are highest weight in our sense. Our main result is an explicit combinatorial description of (the labels of) the crystal on the set of simple objects. A new application of this is to determining the supports of simple modules over the cyclotomic Rational Cherednik algebras starting from their labels.