$t$-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913814188916736 |
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| author | Kashiwara, Masaki Oh, Se-jin |
| author_facet | Kashiwara, Masaki Oh, Se-jin |
| contents | 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 $q=1$ of an arbitrary finite type, called the $t$-quantized Cartan matrix, informs 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $t$-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras Kashiwara, Masaki Oh, Se-jin Representation Theory Quantum Algebra 17B37, 16T30, 17B67 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 $q=1$ of an arbitrary finite type, called the $t$-quantized Cartan matrix, informs 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. |
| title | $t$-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras |
| topic | Representation Theory Quantum Algebra 17B37, 16T30, 17B67 |
| url | https://arxiv.org/abs/2302.08700 |