t-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
- Authors
- Kashiwara, Masaki; Oh, Se-jin
- Issue Date
- Apr-2024
- Publisher
- Academic Press Inc.
- Keywords
- d-invariant; Quiver Hecke algebras; R-matrices; t-quantized Cartan matrix
- Citation
- Advances in Mathematics, v.441
- Indexed
- SCIE
SCOPUS
- Journal Title
- Advances in Mathematics
- Volume
- 441
- URI
- https://scholarworks.bwise.kr/skku/handle/2021.sw.skku/110358
- DOI
- 10.1016/j.aim.2024.109551
- ISSN
- 0001-8708
1090-2082
- 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. © 2024 Elsevier Inc.
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