Singular Light Leaves: A Diagrammatic Basis for Bott-Samelson Bimodules

by Leonardo Patimo (Università di Pisa)

Thursday 22 Feb 2024, 15:00 → 16:00 Europe/Rome

Aula Magna (Department of Mathematics)

Bott-Samelson bimodules correspond geometrically to resolutions of singularities of Schubert varieties. In the nonsingular case, i.e., for Schubert varieties in full flag varieties, Libedinsky introduced a basis (called light leaves) between Bott-Samelson bimodules which has been extensively used to compute the decomposition behavior in the Hecke category, for example enabling the discovery of counterexamples to Lusztig's conjecture on representations in characteristic $p$.
In this talk, we will provide a thorough generalization to the singular setting, which corresponds geometrically to partial flag varieties. We will describe how to construct the basis of singular light leaves using the language of diagrammatic calculus. This construction has concrete applications in computing intersection forms, as well as more theoretical implications. This is a joint project with B. Elias, H. Ko, and N. Libedinsky.