Representations with Zero Infinitesimal Character ================================================== Let :math:`G=Sp(4, \mathbb R)`. We can also compute all the representations with infinitesimal character zero :: atlas> G:Sp(4,R) Variable G: RealForm (overriding previous instance, which had type RealForm) atlas> set parameters=all_parameters_gamma(G,[0,0]) Variable parameters: [Param] (overriding previous instance, which had type [Param]) atlas> #parameters Value: 5 atlas> void: for p in parameters do prints(p) od final parameter (x=0,lambda=[0,0]/1,nu=[0,0]/1) final parameter (x=1,lambda=[0,0]/1,nu=[0,0]/1) final parameter (x=5,lambda=[0,1]/1,nu=[0,0]/1) final parameter (x=6,lambda=[0,1]/1,nu=[0,0]/1) final parameter (x=10,lambda=[2,1]/1,nu=[0,0]/1) atlas> Note that ``nu`` is always ``0``. The last row is the spherical principal series at infinitesimal character ``0`` and ``lambda`` is essentially ``rho``. But this is only telling you what the character is on the :math:`{\mathbb Z}_2` factors. On the other end the first two are the limits of discrete series and we have two intermediate ones. So we only have one principal series at zero infinitesimal character.