Open AccessOn Donkin’s tilting module conjecture I: lowering the prime
Author(s) -
Christopher P. Bendel,
Daniel K. Nakano,
Cornelius Pillen,
Paul Sobaje
Publication year - 2022
Publication title -
representation theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.169
H-Index - 37
ISSN - 1088-4165
DOI - 10.1090/ert/608
Subject(s) - algorithm , annotation , conjecture , artificial intelligence , computer science , mathematics , combinatorics
In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank 2 2 semisimple algebraic groups and SL 4 ( k ) \operatorname {SL}_{4}(k) where k k is an algebraically closed field of characteristic p > 0 p>0 . In the process, new techniques are introduced involving the existence of ( p , r ) (p,r) -filtrations, Lusztig’s character formula, and the G r G_{r} T-radical series for baby Verma modules.