I don't get a grip of what that exactly means. What IS an abstract singlet, doublet,... under SU(N) or other groups?
Answer
"Singlet under SU(N)" means that the related representation is invariant under SU(N).
"Doublet" is related in general to SU(2), and corresponds to the fundamental (2- dimensional) representation of SU(2)
For instance, looking at the "weak interaction", left-handed particles transform as a doublet under SU(2)L , while right-handed particles transform as a singlet under SU(2)L
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