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We study the spectra of G/G coset models by computing BRST cohomology ofaffine 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 theminimal matter coupled to gravity (including boundary states of the Kac table)is observed. This phenomena is discussed from the point of hamiltonianreduction of BRST complexes of $A_N^1$ Lie algebras. (In the revised versionone proof is modified and examplified, some misprints are corrected.)Comment: 16 page

international journal of modern physics a

ON THE SPECTRA OF ${{\widehat{sl}\left( N \right)_k } \mathord{\left/ {\vphantom {{\widehat{sl}\left( N \right)_k } {\widehat{sl}\left( N \right)_k }}} \right. \kern-\nulldelimiterspace} {\widehat{sl}\left( N \right)_k }}$ AND W<sub>N</sub> GRAVITIES

ON THE SPECTRA OF ${{\widehat{sl}\left( N \right)_k } \mathord{\left/ {\vphantom {{\widehat{sl}\left( N \right)_k } {\widehat{sl}\left( N \right)_k }}} \right. \kern-\nulldelimiterspace} {\widehat{sl}\left( N \right)_k }}$ AND WN GRAVITIES

ON THE SPECTRA OF ${{\widehat{sl}\left( N \right)_k } \mathord{\left/ {\vphantom {{\widehat{sl}\left( N \right)_k } {\widehat{sl}\left( N \right)_k }}} \right. \kern-\nulldelimiterspace} {\widehat{sl}\left( N \right)_k }}$ AND W_N GRAVITIES