Discrete-spectrum base-change conjecture for complex symmetric spaces
Discrete-spectrum base-change conjecture for complex symmetric spaces
Let be a real reductive group and let be an irreducible unitary representation of . Discrete-spectrum base-change conjecture. There is at most one pure inner form of over , necessarily the quasi-split inner form, for which occurs in the discrete spectrum of . If it occurs, it has multiplicity one and does not occur in the continuous spectrum for any inner form. The discrete spectrum for is the base change of the discrete spectrum for ; in particular it is tempered and is nonzero exactly when the discrete spectrum for is nonzero, with the final comparison stated in the source when is not an inner form of . This conjecture concerns the spectral decomposition of complex symmetric spaces and is reported as largely known in parts, but no complete resolution is supplied here.
Sources & referencesView supporting material
Primary source
Dipendra Prasad, “A `relative' local Langlands correspondence”, arXiv:1512.04347 (2015).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.