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As every simple module of a quiver Hecke algebra appears as the image of theR-matrix defined on the convolution product of certain cuspidal modules,knowing the $\mathbb{Z}$-invariants of the R-matrices between cuspidal modulesis quite significant. In this paper, we prove that the $(q,t)$-Cartan matrixspecialized at $q=1$ of an arbitrary finite type, called the $t$-quantizedCartan matrix, informs us of the invariants of R-matrices. To prove this, weuse combinatorial AR-quivers associated with Dynkin quivers and theirproperties as crucial ingredients.

$t$-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras