By a result of Hemmer, every simple Specht module of a finite symmetric group
over a field of odd characteristic is a signed Young module. While Specht
modules are parametrized by partitions, indecomposable signed Young modules are
parametrized by certain pairs of partitions. The main result of this article
establishes the signed Young module labels of simple Specht modules. Along the
way we prove a number of results concerning indecomposable signed Young modules
that are of independent interest. In particular, we determine the label of the
indecomposable signed Young module obtained by tensoring a given indecomposable
signed Young module with the sign representation. As consequences, we obtain
the Green vertices, Green correspondents, cohomological varieties, and
complexities of all simple Specht modules and a class of simple modules of
symmetric groups, and extend the results of Gill on periodic Young modules to
periodic indecomposable signed Young modules.Comment: To appear in Adv. Math. 307 (2017) 369--416. Proposition 4.3 (F4),
(F5) corrected, Lemma 4.9 adjusted accordingl