Singularities of normalized R-matrices and E-invariants for Dynkin quivers
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.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Combinatorial Mathematics
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Annals of representation theory
- Volume
- 3
- Issue
- 2
- Pages
- 179–204
- Publication date
- 17 June 2026
- Language
- EN