  We present spectroscopic identification of 32 new quasars and luminous
galaxies discovered at 5.7 < z < 6.8. This is the second in a series of papers
presenting the results of the Subaru High-z Exploration of Low-Luminosity
Quasars (SHELLQs) project, which exploits the deep multi-band imaging data
produced by the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey. The
photometric candidates were selected by a Bayesian probabilistic algorithm, and
then observed with spectrographs on the Gran Telescopio Canarias and the Subaru
Telescope. Combined with the sample presented in the previous paper, we have
now identified 64 HSC sources over about 430 deg2, which include 33 high-z
quasars, 14 high-z luminous galaxies, 2 [O III] emitters at z ~ 0.8, and 15
Galactic brown dwarfs. The new quasars have considerably lower luminosity
(M1450 ~ -25 to -22 mag) than most of the previously known high-z quasars.
Several of these quasars have luminous (> 10^(43) erg/s) and narrow (< 500
km/s) Ly alpha lines, and also a possible mini broad absorption line system of
N V 1240 in the composite spectrum, which clearly separate them from typical
quasars. On the other hand, the high-z galaxies have extremely high luminosity
(M1450 ~ -24 to -22 mag) compared to other galaxies found at similar redshift.
With the discovery of these new classes of objects, we are opening up new
parameter spaces in the high-z Universe. Further survey observations and
follow-up studies of the identified objects, including the construction of the
quasar luminosity function at z ~ 6, are ongoing.
