  We study the spectra of G/G coset models by computing BRST cohomology of
affine Lie algebras with coefficients in tensor product of two modules.
One-to-one correspondence between the spectra of $A_1^1/A_1^1$ and that of the
minimal matter coupled to gravity (including boundary states of the Kac table)
is observed. This phenomena is discussed from the point of hamiltonian
reduction of BRST complexes of $A_N^1$ Lie algebras. (In the revised version
one proof is modified and examplified, some misprints are corrected.)
