Schubert calculus and torsion explosion

By Geordie Williamson. 2013

140 citations recorded by the source corpus.

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

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/94e8c1f7c8d08f9a6f5a5526d214057a21761468

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In Discrete Mathematics and Combinatorics

1. L. T. Jensen
2. Geordie Williamson
3. Ben Elias
4. Simon Riche

In Geometry and Topology

1. L. T. Jensen
2. Geordie Williamson
3. Ben Elias
4. Simon Riche

In Mathematical Physics

1. L. T. Jensen
2. Geordie Williamson
3. Ben Elias

Citations in the corpus

• The $p$-Canonical Basis for Hecke Algebras (2015, background): “ the p-canonical basis, and then one should calculate the p-canonical basis. In general the second step seems to be extremely dicult, and it is possibly too optimistic to expect an answer in general [Wil13]. However at the very least this approach has the potential to unify questions in modular repr”