A Hall-algebra calculation gives a complete classification, including multiplicities, of Hecke modifications of split vector bundles on P^1 over finite fields, plus an elementary proof that unramified toroidal automorphic forms for PGL_n vanish.
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Hall algebras and Hecke modifications of vector bundles
A Hall-algebra calculation gives a complete classification, including multiplicities, of Hecke modifications of split vector bundles on P^1 over finite fields, plus an elementary proof that unramified toroidal automorphic forms for PGL_n vanish.