Singularities of normalized R-matrices and E-invariants for Dynkin quivers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917829435981824 |
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| author | Fujita, Ryo |
| author_facet | Fujita, Ryo |
| contents | We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using equivariant perverse sheaves, following the previous works by Nakajima [Kyoto J. Math. 51(1), 2011] and Kimura--Qin [Adv. Math. 262, 2014]. We show that the pole orders of these R-matrices coincide with the dimensions of E-invariants between the corresponding decorated representations of Dynkin quivers. This result can be seen as a correspondence of numerical characteristics between additive and monoidal categorifications of cluster algebras of finite ADE type. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10070 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularities of normalized R-matrices and E-invariants for Dynkin quivers Fujita, Ryo Representation Theory Quantum Algebra 17B37, 18M05, 16G20, 13F60 We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using equivariant perverse sheaves, following the previous works by Nakajima [Kyoto J. Math. 51(1), 2011] and Kimura--Qin [Adv. Math. 262, 2014]. We show that the pole orders of these R-matrices coincide with the dimensions of E-invariants between the corresponding decorated representations of Dynkin quivers. This result can be seen as a correspondence of numerical characteristics between additive and monoidal categorifications of cluster algebras of finite ADE type. |
| title | Singularities of normalized R-matrices and E-invariants for Dynkin quivers |
| topic | Representation Theory Quantum Algebra 17B37, 18M05, 16G20, 13F60 |
| url | https://arxiv.org/abs/2410.10070 |