Categorical geometric symmetric Howe duality

TL;DR

This paper develops a geometric framework for symmetric Howe duality using loop sl(n) actions on derived categories of coherent sheaves, extending previous work on categorical sl(n) actions and skew Howe duality.

Contribution

It introduces a natural geometric setting for symmetric Howe duality via loop sl(n) actions on derived categories, linking it to earlier skew Howe duality work.

Findings

Established a geometric realization of symmetric Howe duality.

Connected symmetric and skew Howe duality through geometric actions.

Extended categorical sl(n) actions to new geometric contexts.

Abstract

We provide a natural geometric setting for symmetric Howe duality. This is realized as a (loop) sl(n) action on derived categories of coherent sheaves on certain varieties arising in the geometry of the Beilinson-Drinfeld Grassmannian. The main construction parallels our earlier work on categorical sl(n) actions and skew Howe duality. In that case the varieties involved arose in the geometry of the affine Grassmannian. We discuss some relationships between the two actions.