arXiv: Representation Theory | 2019
On character formulas for simple and tilting modules.
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 $G$.