Strange duality at level one for alternating vector bundles

TL;DR

This paper proves a strange duality isomorphism at level one for generalized theta functions on moduli spaces of alternating anti-invariant vector bundles, a significant case involving non-trivial parahoric G-torsors.

Contribution

It establishes a new strange duality isomorphism at level one for a specific class of vector bundles related to twisted parahoric G-torsors.

Findings

Strange duality isomorphism at level one proven for these bundles.

Extension of duality results to ramified cases with non-trivial parahoric structures.

Provides new insights into the geometry of moduli spaces of anti-invariant vector bundles.

Abstract

In this paper, we show a strange duality isomorphism at level one for the space of generalized theta functions on the moduli spaces of alternating anti-invariant vector bundles in the ramified case. These anti-invariant vector bundles constitute one of the non-trivial examples of parahoric G-torsors, where G is a twisted (not generically split) parahoric group scheme.