Schubert calculus and torsion explosion

Geordie Williamson, Alex Kontorovich, Peter J. McNamara

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1023-1046
Number of pages24
JournalJournal of the American Mathematical Society
Volume30
Issue number4
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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