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Elliptic Characteristic classes o matrix Schubert varieties: patterns and algebra

Algebraic Geometry and Number Theory Seminar

Date: Thursday, October 19, 2023 13:00 - 15:00
Speaker: Andrzej Weber (University of Warsaw)
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series: Mathematics and CS Seminar
Host: Kamil Rychlewicz

We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties and B-orbits of square-zero matrices. The first family is governed by permutations, the second by partial permutations and the last one by "patterns".  Schubert varieties admit  certain characteristic classes in equivariant elliptic cohomology obtained within the framework created by Borisov and Libgober. Elliptic characteristic classes satisfy Okounkov axioms of stable envelopes. We consider the Hecke-type algebra computing elliptic classes and extend its action to partial permutations and patterns. An uniform point of view allows to understand duality better.


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