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Modular Branching Rules and the Mullineux Map for Hecke Algebras of Type A
Author(s) -
Brundan J
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000562
Subject(s) - mathematics , subalgebra , pure mathematics , branching (polymer chemistry) , irreducible representation , hecke operator , hecke algebra , modular design , type (biology) , involution (esoterism) , representation theory , algebra over a field , modular form , computer science , politics , political science , law , operating system , ecology , materials science , composite material , biology
We prove the quantum version ‐ for Hecke algebras H A n of type A at roots of unity ‐ of Kleshchev's modular branching rule for symmetric groups. This result describes the socle of the restriction of an irreducible H A n ‐module to the subalgebra H A n−1 . As a consequence, we describe the quantum version of the Mullineux involution describing the irreducible module obtained on twisting an irreducible module with the sign representation. 1991 Mathematics Subject Classification : 20C05, 20G05.