Let \(\pi_1,\ldots,\pi_n\) denote essentially Speh representations and \(\pi_A\) a representation of Arthur type of an special odd orthogonal or symplectic group over a non-archimedean local field. In this talk we will describe an irreducibility criterion for the induced representation \(\pi_1\times\cdots\times\pi_n\rtimes\pi_A\) in terms of the irreducibility of representations induced by two representations from the set \(\{\pi_i,\tilde{\pi_i},\pi_A: i=1,\ldots,n\}\). We will also comment on the methods of the proof. In the unitary case, they are based on the theory of extended multi-segments. In the non-unitary case, we use H. Atobe's results on the socle of and induced representation of the form \pi\rtimes\pi_A.
An irreducibility criterion for representations induced from essentially Speh representations and a representation of Arthur type
14.05.2024 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: