Relationship between Mullineux involution and the generalized regularization. (March 2020)

• Record Type: Journal Article
• Authors: Wang, Allen; Yue, Guangyi
• Is Part Of: European journal of combinatorics. Volume 85(2020)
• Publication Date: 2020-03
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2019.103059
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: The Mullineux involution is an important map on p -regular partitions that originates from the modular representation theory of S n . In this paper we study the Mullineux transpose map and the generalized column regularization and prove a condition under which the two maps are exactly the same. Our results generalize the work of Bessenrodt, Olsson and Xu, and the combinatorial constructions is related to the Iwahori–Hecke algebra and the global crystal basis of the basic U q ( sl ̂ b ) -module. In the conclusion, we provide several conjectures regarding the q -decomposition numbers and generalizations of results due to Fayers.