Dual exceptional collections on Lagrangian Grassmannians

TL;DR

This paper constructs dual exceptional collections on Lagrangian Grassmannians and uses them to derive explicit resolutions for certain equivariant vector bundles, advancing the understanding of their geometric and algebraic structures.

Contribution

It introduces graded left dual exceptional collections on Lagrangian Grassmannians, providing new tools for studying vector bundles on these spaces.

Findings

Constructed graded left dual exceptional collections.

Derived explicit resolutions for natural equivariant vector bundles.

Enhanced understanding of the derived category structure of Lagrangian Grassmannians.

Abstract

We construct graded left dual exceptional collections to the exceptional collections generating the blocks of Kuznetsov and Polishchuk on Lagrangian Grassmannians. As an application, we find explicit resolutions for some natural irreducible equivariant vector bundles.