We consider mixing of the antidecuplet with three J^P=1/2^+ octets (the
ground-state octet, the octet containing N(1440), \Lambda(1600), \Sigma(1660)
and \Xi(1690) and the octet containing N(1710), \Lambda(1800), \Sigma(1880) and
\Xi(1950)) in the framework of approximate flavor SU(3) symmetry. We give
general expressions for the partial decay widths of all members of the
antidecuplet as functions of the two mixing angles. Identifying N_{anti-10}
with the N(1670) observed by the GRAAL experiment, we show that the considered
mixing scenario can accommodate all present experimental and phenomenological
information on the \Theta^+ and N_{anti-10} decays: \Theta^+ could be as narrow
as 1 MeV; the N_{anti-10} -> N + \eta decay is sizable, while the N_{anti-10}
->N + \pi decay is suppressed and the N_{anti-10} ->\Lambda + K decay is
possibly suppressed. Constraining the mixing angles by the N_{anti-10} decays,
we make definite predictions for the \Sigma_{anti-10} decays. We point out that
\Sigma_{anti-10} with mass near 1770 MeV could be searched for in the available
data on K_S p invariant mass spectrum, which already revealed the \Theta^+
peak. It is important to experimentally verify the decay properties of
\Sigma(1770) because its mass and J^P=1/2^+ make it an attractive candidate for
\Sigma_{anti-10}.Comment: 57 pages, 31 figures, 4 table
