Crossingless sheaves and their classes in equivariant K-theory

TL;DR

This paper introduces crossingless sheaves in equivariant derived categories, analogous to exotic sheaves, and computes their classes in the equivariant K-theory of Cautis-Kamnitzer varieties, advancing understanding in geometric representation theory.

Contribution

It defines crossingless sheaves in equivariant derived categories and calculates their classes in equivariant K-theory, extending the theory of exotic sheaves to new settings.

Findings

Defined crossingless sheaves in equivariant derived categories.

Computed classes of these sheaves in equivariant K-theory.

Extended the analogy of exotic sheaves to new varieties.

Abstract

We introduce crossingless sheaves in certain equivariant derived categories which are analogous to the Bezrukavnikov-Mirkovic exotic sheaves for two-block nilpotents. We calculate the classes of crossingless sheaves in equivariant K-theory of Cautis-Kamnitzer varieties.