  We present the first central velocity dispersions (sigma_o) measured from the
0.85 micron Calcium II Triplet (CaT) for 8 advanced (i.e. single nuclei) local
(z < 0.15) Ultraluminous Infrared Galaxies (ULIRGs). First, these measurements
are used to test the prediction that the "sigma-Discrepancy," in which the CaT
sigma_o is systematically larger than the sigma_o obtained from the 1.6 or 2.3
micron stellar CO band-heads, extends to ULIRG luminosities. Next, we combine
the CaT data with rest-frame I-band photometry obtained from archival Hubble
Space Telescope data and the Sloan Digital Sky Survey (SDSS) to derive
dynamical properties for the 8 ULIRGs. These are then compared to the dynamical
properties of 9,255 elliptical galaxies from the SDSS within the same redshift
volume and of a relatively nearby (z < 0.4) sample of 53 QSO host galaxies. A
comparison is also made between the I-band and H-band dynamical properties of
the ULIRGs. We find four key results: 1) the sigma-Discrepancy extends to ULIRG
luminosities; 2) at I-band ULIRGs lie on the Fundamental Plane (FP) in a region
consistent with the most massive elliptical galaxies and not low-intermediate
mass ellipticals as previously reported in the near-infrared; 3) the I-band M/L
of ULIRGs are consistent with an old stellar population, while at H-band ULIRGs
appear significantly younger and less massive; and 4) we derive an I-band
Kormendy Relation from the SDSS ellipticals and demonstrate that ULIRGs and QSO
host galaxies are dynamically similar.
