Singularities of Schubert varieties within a right cell

Martina Lanini and I recently posted our preprint Singularities of Schubert varieties within a right cell to the arXiv. In it, we show that every singularity which appears in a type A Schubert variety appears between two permutations lying in the same right cell. This shows that any behaviour controlled by the singularities of Schubert varieties manifests itself within a Specht module. Some exmples are discussed.

The work was conducted during our recent visit to the thematic trimester program on representation theory at the Institut Henri Poincaré in Paris. I spent an enjoyable first month there before returning to Australia. Originally I was scheduled to be on a plane right now to return to Paris for the end of the program, but alas this is no longer possible. Oh well.