On Donkin’s tilting module conjecture I: lowering the prime
نویسندگان
چکیده
In this paper the authors provide a complete answer to Donkin’s Tilting Module Conjecture for all rank 2 2 semisimple algebraic groups and alttext="upper S upper L 4 left-parenthesis k right-parenthesis"> SL 4 ( k stretchy="false">) encoding="application/x-tex">\operatorname {SL}_{4}(k) where alttext="k"> encoding="application/x-tex">k is an algebraically closed field of characteristic alttext="p greater-than 0"> p > 0 encoding="application/x-tex">p>0 . process, new techniques are introduced involving existence alttext="left-parenthesis p comma r , r encoding="application/x-tex">(p,r) -filtrations, Lusztig’s character formula, G Subscript r"> G encoding="application/x-tex">G_{r} T-radical series baby Verma modules.
منابع مشابه
Tilting in module categories
Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples ...
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ژورنال
عنوان ژورنال: Representation Theory of The American Mathematical Society
سال: 2022
ISSN: ['1088-4165']
DOI: https://doi.org/10.1090/ert/608