Dec 9, 2021

Elliptic characteristic classes of Schubert varieties and duality

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Date: December 9, 2021 | 2:00 pm – 4:00 pm
Speaker: Andrzej Weber, University of Warsaw
Location: https://mathseminars.org/seminar/AGNTISTA

We modify the theory of Borisov and Libgober to define equivariant characteristic classes of Schubert varieties in the generalized flag varieties G/B. The resulting classes can be considered as functions depending on two sets of parameters: equivariant variables and Kaehler variables. There are two recursions which allow to compute inductively these classes: right recursion corresponding to geometric Demazure-Lusztig operation and left recursion induced by the R-matrix appearing in Yang-Baxter equation. When one passes from a group G to its Langlands' dual the recursions switch they roles. This allows to show that equivariant elliptic classes for Langlands dual groups coincide after a swap of equivariant variables with Kaehler variables. This duality is only on the numerical level. The geometric cause remains mysterious.

More Information:

Date:
December 9, 2021
2:00 pm – 4:00 pm

Speaker:
Andrzej Weber, University of Warsaw

Location:
https://mathseminars.org/seminar/AGNTISTA

Contact:

Birgit Oosthuizen-Noczil

Email:
birgit.oosthuizen-noczil@ist.ac.at

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