Abstract: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.
From: Ryo Fujita [view email]
[v1]
Mon, 14 Oct 2024 01:24:55 UTC (27 KB)
[v2]
Wed, 6 Nov 2024 03:11:32 UTC (27 KB)
[v3]
Thu, 25 Jun 2026 15:14:56 UTC (30 KB)
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