  Within the microscopic model based on the algebraic version of the resonating
group method the role of the Pauli principle in the formation of continuum wave
function of nuclear systems composed of three identical $s$-clusters has been
investigated. Emphasis is placed upon the study of the exchange effects
contained in the genuine three-cluster norm kernel. Three-fermion, three-boson,
three-dineutron ($3d'$) and $3\alpha$ systems are considered in detail. Simple
analytical method of constructing the norm kernel for $3\alpha$ system is
suggested. The Pauli-allowed basis functions for the $3\alpha$ and $3d'$
systems are given in an explicit form and asymptotic behavior of these
functions is established. Complete classification of the eigenfunctions and the
eigenvalues of the $^{12}$C norm kernel by the $^8$Be$=\alpha+\alpha$
eigenvalues has been given for the first time. Spectrum of the $^{12}$C norm
kernel is compared to that of the $^{5}$H system.
