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Let $K$ be an algebraically closed field with $Char K\neq 2$ and $(s_1, s_2,\cdots, s_r)\in \mathbb{Z}^r$ a multicharge with $r>2$. Let $\mathcal {H}_n(q,Q)$ be a cyclotomic Hecke algebra of type $G(r, 1, n)$, where $q\neq 0, 1$ and$Q=(q^{s_1}, q^{s_2}, \cdots, q^{s_r})$. For each block $B$ of $\mathcal{H}_n(q, Q)$, we introduce a new invariant, called block move vector, which canbe considered as a generalization of the weight $w(B)$. We prove by using blockmove vector that block $B$ has finite representation type if and only if$w(B)<2$, or $B$ is Morita equivalent to $K[x]/x^{w(B)+1}$. Blocks of finiterepresentation type with weight more than one are determined completely byblock move vectors. This result implies that some blocks of finite type areBrauer tree algebras whose Brauer trees have exceptional vertex. We alsodetermine representation type for all the blocks of cyclotomic $q$-Schuralgebras. Moreover, by using our result, we construct examples of blocks withthe same weight that are not derived equivalent. Examples of derived equivalentblocks being in different orbits under the adjoint action of the affine Weylgroup are also given.

Representation type of blocks of cyclotomic Hecke algebras of type $G(r, 1, n)$