Laura Escobar (WUSL)

Determining the complexity of Kazhdan-Lusztig varieties


Kazhdan-Lusztig varieties are defined by ideals generated by certain minors of a matrix, which are chosen using a combinatorial rule. These varieties are of interest in commutative algebra and the study of Schubert varieties. Each Kazhdan-Lusztig variety has a natural torus action from which one can construct a polyhedral cone. The complexity of this torus action can be computed from the dimension of the cone and, in some sense, indicates how close the variety is to the toric variety of the cone. In joint work with Maria Donten-Bury and Irem Portakal we address the problem of classifying which Kazhdan-Lusztig varieties have a given complexity. We do so by utilizing the rich combinatorics of Kazhdan-Lusztig varieties.