Exceptional collections on isotropic Grassmannians

TL;DR

This paper introduces a new method for constructing exceptional objects in the derived category of isotropic Grassmannians, leading to full exceptional collections on these spaces for all classical groups.

Contribution

It provides a novel construction of exceptional collections on isotropic Grassmannians, expanding the understanding of their derived categories.

Findings

Constructs exceptional collections of length equal to the Grothendieck group rank.

Applies to homogeneous spaces of all classical groups.

Advances the classification of derived categories for isotropic Grassmannians.

Abstract

We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.