Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 283-325.

ON REDUCIBILITY OF REPRESENTATIONS INDUCED FROM THE ESSENTIALLY SPEH REPRESENTATIONS AND DISCRETE SERIES

Ivan Matić

Abstract.   Let π stand for an essentially Speh representation of the form L(δ([ν^a ρ, ν^a+k ρ]), ..., δ([ν^a+n-1 ρ, ν^a+k+n-1} ρ])), where ρ is an irreducible cuspidal representation of the general linear group over a non-archimedean local field or its separable quadratic extension, a ≤ 0, 2a + k > 0, and n ≥ 1. Let σ denote a discrete series representation of either symplectic, special odd-orthogonal, or unitary group. We determine when the induced representation π ⋊ σ reduces.

2020 Mathematics Subject Classification.   22E35, 22E50, 11F70.

Key words and phrases.   Classical p-adic groups, essentially Speh representations, discrete series.

DOI: https://doi.org/10.21857/ypn4oc4q59

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