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We study infinitely many commuting operators $T_B(z)$, which we call infinitetransfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model. We diagonalizeinfinite transfer matrix $T_B(z)$ by using free field realizations of thevertex operators of the elliptic quantum group $U_{q,p}(A_{N-1}^{(1)})$.

Diagonalization of infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model