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We study the relationship between Calogero-Moser cellular characters andcharacters defined from vectors of a Fock space of type $A_{\infty}$. Usingthis interpretation, we show that Lusztig's constructible characters of theWeyl group of type $B$ are sums of Calogero-Moser cellular characters. We alsogive an explicit construction of the character of minimal $b$-invariant of agiven Calogero-Moser family of the complex reflection group $G(l,1,n)$.

On Calogero-Moser cellular characters for imprimitive complex reflection groups