On Classical groups detected by the tensor third representation

Original · EN

Motivated by the Langlands' beyond endoscopy proposal for establishing functoriality, we study the representation ⊗³ in a setting related to the Langlands L-functions L(s,π,⊗³), where π is a cuspidal automorphic representation of G where G is either SO(2n+1), Sp(2n) and SO(2n). In particular, under what conditions on partitions λ, we examine whether or not ⊗³ detects the subgroups S[λ](G) for G with type Bₙ and D₂ₙ or Sλ(G) for G with type Cₙ. Here S[λ] and Sλ are the usual Schur functors associated to the partition λ.