Half-integrality of line bundles on partial flag schemes of classical Lie groups

Abstract

In this paper, we develop a theory of Galois descent for equivariant line bundles on partial flag schemes. In particular, we study computational aspects of the classification of descent data of equivariant line bundles attached to characters of parabolic subgroups. As an application, we classify equivariant line bundles on partial flag schemes of the standard $\mathbb{Z}\left[1/2\right]$-forms of classical Lie groups.

Typos were corrected

Cited by in corpus (5)

• Classification of irreducible representations of affine group superschemes and the division superalgebras of their endomorphisms
• Uniform decomposition of the flag scheme by a symmetric subgroup action
• Rationality patterns
• Filtrations on the globalization of twisted D-modules over Dedekind schemes
• $\mathrm{SO}(3)$-homogeneous decomposition of the flag scheme of ${\mathrm{SL}}_3$ over $\mathbb{Z}\left[1/2\right]$