\(t\)-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras.(English)Zbl 07823123
Summary: As every simple module of a quiver Hecke algebra appears as the image of the R-matrix defined on the convolution product of certain cuspidal modules, knowing the \(\mathbb{Z}\)-invariants of the R-matrices between cuspidal modules is quite significant. In this paper, we prove that the \((q, t)\)-Cartan matrix specialized at \(q = 1\) ofany finite type, called the\(t\)-quantized Cartan matrix, inform us of the invariants of R-matrices. To prove this, we use combinatorial AR-quivers associated with Dynkin quivers and their properties as crucial ingredients.
MSC:
| 16T30 | Connections of Hopf algebras with combinatorics |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
Cite
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