  The elegant predictions of loop quantum gravity are obscured by the free
Immirizi parameter. Dreyer (2003), considering the asymptotic quasinormal modes
spectrum of a black hole, proposed that the Immirizi parameter may be fixed by
letting the j=1 transitions of spin networks as the dominant processes
contributing to the black hole area, as opposed to the expected j=1/2
transitions. This suggested that the gauge group of the theory might be SO(3)
rather than SU(2). Corichi (2003), maintaining SU(2) as the underlying gauge
group, and invoking the principle of local fermion-number conservation,
reported the same value of the Immirizi parameter for j=1 processes as obtained
by Dreyer. In this note, preserving the SU(2) structure of the theory, and
considering j=1 transitions as the dominant processes, we point out that the
value of the Immirizi parameter is in fact twice the value reported by these
authors. We arrive at this result by assuming the asymptotic quasinormal modes
themselves as dynamical systems obeying SU(2) symmetry.
