Vanishing linear periods of cuspidal automorphic sheaves for 𝐺𝐿_{𝑚+𝑛}

Abstract

In this paper, we prove a vanishing theorem concerning the periods of cuspidal automorphic sheaves for GL m + n \operatorname {GL}_{m+n} along the Levi subgroup GL m × GL n \operatorname {GL}_{m}\times \operatorname {GL}_{n} for m ≠ n m \neq n .