Work

Singularities of normalized R-matrices and E-invariants for Dynkin quivers

Year: 2026

Type: article

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.

Source: Annals of representation theory

DOI: 10.5802/art.39

Author: Ryo Fujita

Institutions: Kyoto University, Research Institute for Mathematical Sciences, Kyoto University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: Study on the representations of affine quantum groups using quivers with potentials