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 A1(1)/A1(1) and that of the minimal matter coupled to gravity (including boundary states of the Kac table) is observed. This phenomenon is discussed from the point of Hamiltonian reduction of BRST complexes of A(N)1 Lie algebras.