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The duality principle for group representations developed in \cite{DHL-JFA,HL_BLM} exhibits a fact that the well-known duality principle in Gabor analysisis not an isolated incident but a more general phenomenon residing in thecontext of group representation theory. There are two other well-knownfundamental properties in Gabor analysis: The Wexler-Raz biorthogonality andthe Fundamental Identity of Gabor analysis. In this paper we will show thatthese fundamental properties remain to be true for general projective unitarygroup representations. The main purpose of this paper is present a more generalduality theorem which shows that that muti-frame generators meet super-framegenerators through a dual commutant pairs. In particular, for the Gaborrepresentations $\pi_{\Lambda}$ and $\pi_{\Lambda^{o}}$ with respect to a pairof dual time-frequency lattices $\Lambda$ and $\Lambda^{o}$ in $\R^{d}\times\R^{d}$ we have that $\{\pi_{\Lambda}(m, n)g_{1} \oplus ... \oplus\pi_{\Lambda}(m, n)g_{k}\}_{m, n \in \Z^{d}}$ is a frame for$L^{2}(\R^{d})\oplus ... \oplus L^{2}(\R^{d})$ if and only if$\cup_{i=1}^{k}\{\pi_{\Lambda^{o}}(m, n)g_{i}\}_{m, n\in\Z^{d}}$ is a Rieszsequence, and $\cup_{i=1}^{k}\{\pi_{\Lambda}(m, n)g_{i}\}_{m, n\in\Z^{d}}$ is aframe for $L^{2}(\R^{d})$ if and only if $\{\pi_{\Lambda^{o}}(m, n)g_{1} \oplus... \oplus \pi_{\Lambda^{o}}(m, n)g_{k}\}_{m, n \in \Z^{d}}$ is a Rieszsequence. This appears to be new even in the context of Gabor analysis.

A duality principle for groups II: Multi-frames meet super-frames