On Donkin’s tilting module conjecture I: lowering the prime | Zendy

Christopher P. Bendel | Zendy; Daniel K. Nakano | Zendy; Cornelius Pillen | Zendy; Paul Sobaje | Zendy

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On 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 of the american mathematical society

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.

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