Unitary principal series of split orthogonal groups (Q473117)

The authors show that the set of unitary principal series parameters for the group \(\mathrm{SO}(n+1,n)\) embeds into the union of spherical unitary parameters for certain split orthogonal groups. As the latter set is known, the result implies nonunitarity of a large set of parameters for Langlands quotients of minimal principal series of \(\mathrm{SO}(n+1,n)\). The authors conjecture that the set of unitary parameters obtained in this way is, in fact, complete and prove this for small rank groups and for unipotent parameters.