Reduction Theory for a Rational Function Field

[摘要] Let 𝐺 be a split reductive group over a finite field $F_q$. Let $F = F_q(t)$ and let 𝐴 denote the adèles of 𝐹. We show that every double coset in $G(F)ackslash G(A)/K$ has a representative in a maximal split torus of 𝐺. Here 𝐾 is the set of integral adèlic points of 𝐺. When 𝐺 ranges over general linear groups this is equivalent to the assertion that any algebraic vector bundle over the projective line is isomorphic to a direct sum of line bundles.

[学科分类] 数学（综合）

[关键词] Automorphic form;function field.