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- Title
- t-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
- KIAS Author
- Kashiwara, Masaki
- Journal
- ADVANCES IN MATHEMATICS, 2024
- Archive
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- Abstract
- 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 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 of any 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. (c) 2024 Elsevier Inc. All rights reserved.