Schubert calculus and torsion explosion

The author observes that certain numbers occurring in Schubert calculus for SL n SL_n also occur as entries in intersection forms controlling decompositions of Soergel bimodules in higher rank. These numbers grow exponentially. This observation gives many counter-examples to the expected bounds in Lusztig’s conjecture on the characters of simple rational modules for SL n SL_n over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.