Relationship between Mullineux involution and the generalized regularization

The Mullineux involution is an important map on pregular partitions that originates from the modular representation theory of \mathcal{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...