Constructs irreducible cuspidal-like representations for PGL(2,K) from quadratic extensions L/K and non-Galois-invariant characters, proving their restrictions to Borel subgroups are irreducible but not isomorphic to standard cuspidals.
Hsie,Mackey Theory for p-adic Lie Groups, Acta Mathematica Sinica, English Series, Volume 22, Issue 2, 2006, pages 507–514
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An analogue of irreducible cuspidal representations for the group $PGL(2)$ over a two-dimensional local field
Constructs irreducible cuspidal-like representations for PGL(2,K) from quadratic extensions L/K and non-Galois-invariant characters, proving their restrictions to Borel subgroups are irreducible but not isomorphic to standard cuspidals.