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Elliptic characteristic classes of Schubert varieties and duality


Date: Thursday, December 9, 2021 14:00 - 16:00
Speaker: Andrzej Weber (University of Warsaw)
Location: https://mathseminars.org/seminar/AGNTISTA
Series: Mathematics and CS Seminar
Host: Tamas Hausel

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.

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