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.
Automorphic forms for PGL(3) over elliptic function fields. Part 1: Graphs of Hecke operators
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This is a first part of a series of papers in which we develop explicit computational methods for automorphic forms for GL(3) and PGL(3) over elliptic function fields. In this first part, we determine explicit formulas for the action of the Hecke operators on automorphic forms on GL(2) and GL(3) in terms of their graphs. Our primary result consists in a complete description of the graphs of degree 1 Hecke operators for GL(3). As complementary results, we describe the 'even component' of the graphs of degree 2 Hecke operators for GL(2) and the 'neighborhood of the identity' of the graphs of degree 2 Hecke operators for GL(3). In addition, we establish two dualities for Hecke operators for GL(n) and PGL(n), which hold for all n, all degrees and all function fields.
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.