The irreducibility criterion for representations induced from the essentially Speh representations and the representation of Arthur type

Barbara Bošnjak (U Zagreb)

Sep 05. 2025, 10:00 — 10:45

Let $\pi,\pi_1,\ldots,\pi_n$ denote the essentially Speh representations and $\pi_A$ the representation of the Arthur type of the special odd orthogonal or symplectic group over a non-archimedean local field. In this talk we will describe the 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 the induced representation $\pi\rtimes\pi_A$ .

Further Information

Venue:: ESI Boltzmann Lecture Hall
Associated Event:: Eisenstein Series, Spaces of Automorphic Forms, and Applications (Workshop)
Organizer(s):: Neven Grbac (UNIPU)
Marcela Hanzer (U Zagreb)
Stephen S. Kudla (U Toronto)
Joachim Schwermer (U of Vienna)