Lusztig varieties can be seen as variants of both Schubert varieties and Hessenberg varieties. For example, they admit a Weyl group action on their intersection cohomology through monodromy, and their singularities can be resolved via Bott-Samelson-type resolutions. I will present results on their geometry, including vanishing theorems for the cohomology of line bundles, their relations to Hessenberg varieties, and diffeomorphism types. Along the way, we also establish that their open cells are affine, and that the same is true for Deligne-Lusztig varieties, settling a question that has been open since the foundational paper of Deligne and Lusztig. Some of the results were motivated by our forthcoming study of the Weyl group representations via a trace map of the Hecke algebra. Based on joint works with Patrick Brosnan and Jaehyun Hong.
Geometry of regular semisimple Lusztig varieties
07.10.2025 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: