Link patterns and elliptic Hecke algebra

We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is governed by permutations, the second by partial permutations, and the last one by “link patterns”. These geometric objects admit characteristic classes in equivariant elliptic cohomology obtained within the framework created by Borisov and Libgober. We construct a Hecke-type algebra for computing elliptic classes and extend its action to include partial permutations and linking patterns. A uniform point of view facilitates a better understanding of duality.