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arXiv · 1902.10308

On character formulas for simple and tilting modules

Paul Sobaje
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Abstract

We show that the characters of tilting modules can be used, in a concrete and explicit way, to obtain the simple characters of a connected reductive algebraic group $G$ over an algebraically closed field $\Bbbk$ of characteristic $p$, for all $p$. Thus, once a formula for the characters of the indecomposable tilting $G$-modules has been found, a formula for the simple modules has been also. An immediate implication is that the work of Achar, Makisumi, Riche, and Williamson in \cite{AMRW} provides a character formula for simple $G$-modules when $p>h$, the Coxeter number of $G$.

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Paul Sobaje. 2019-02-27. On character formulas for simple and tilting modules. https://arxiv.org/abs/1902.10308

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