Schubert calculus and torsion explosion

Williamson, Geordie¹

¹Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

Journal of the American Mathematical Society, Tome 30 (2017) no. 4, pp. 1023-1046

Résumé

The author observes that certain numbers occurring in Schubert calculus for $\text {SL}_n$ 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 $\text {SL}_n$ over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.

Détail

DOI : 10.1090/jams/868

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