Representing the big tilting sheaves as holomorphic Morse branes

TL;DR

This paper introduces Morse branes in the Fukaya category of holomorphic symplectic manifolds to construct tilting objects, specifically representing big tilting sheaves on flag varieties.

Contribution

It develops a new method for constructing tilting objects using Morse branes in the Fukaya category of cotangent bundles.

Findings

Constructed Morse branes in cotangent bundles.

Represented big tilting sheaves as holomorphic branes.

Provided a new approach to tilting object construction in symplectic geometry.

Abstract

We introduce Morse branes in the Fukaya category of a holomorphic symplectic manifold, with the goal of constructing tilting objects in the category. We give a construction of a class of Morse branes in the cotangent bundles, and apply it to give the holomorphic branes that represent the big tilting sheaves on flag varieties.