SCHUBERT CALCULUS AND TORSION EXPLOSION

The author observes that certain numbers occurring in Schubert calculus for SLn 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 SLn over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups. © 2016 American Mathematical Society.