  We report the recent results of the magnetic transitions and axial-vector
transitions of the baryon antidecuplet within the framework of the chiral
quark-soliton model. The dynamical model parameters are fixed by experimental
data for the magnetic moments of the baryon octet, for the hyperon semileptonic
decay constants, and for the singlet axial-vector constant. The transition
magnetic moments $\mu_{\Lambda\Sigma}$ and $\mu_{N\Delta}$ are well reproduced
and other octet-decuplet and octet-antidecuplet transitions are predicted. In
particular, the present calculation of $\mu_{\Sigma\Sigma^*}$ is found to be
below the upper bound $0.82\mu_N$ that the SELEX collaboration measured very
recently. The results explains consistently the recent findings of a new $N^*$
resonance from the GRAAL and Tohoku LNS group. We also obtain the transition
axial-vector constants for the $\Theta^+\to KN$ from which the decay width of
the $\Theta^{+}$ pentaquark baryon is determined as a function of the
pion-nucleon sigma term $\Sigma_{\pi N}$. We investigate the dependence of the
decay width of the $\Theta^{+}$ on the $g_{A}^{(0)}$, with the $g_{A}^{(0)}$
varied within the range of the experimental uncertainty. We show that a small
decay width of the $\Theta^{+}\to KN$, i.e. $\Gamma_{\Theta KN} \leq 1$ MeV, is
compatible with the values of all known semileptonic decays with the generally
accepted value of $g_{A}^{(0)} \approx 0.3$ for the proton.
