Perverse sheaves and quantum Grothendieck rings

2001/03/27 by Michela Varagnolo, Varagnolo, Michela, Éric Vasserot +2 · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0103182

20 pages

openalex publication_date 2001/03/27 · arxiv created 2001/04/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a quantum analogue of the Grothendieck ring of finite dimensional modules of a quantum affine algebra of simply laced type. The construction is based on perverse sheaves on a variety related to quivers. We get also a new geometric construction of the tensor category of finite dimensional modules of a finite dimensional simple Lie algebra of type A-D-E.

Cited by

• Representations and characters of quantum affine algebras at the crossroads between cluster categorification and quantum integrable models
• An introduction to representation-theoretic canonical bases of cluster algebras
• Quantum cluster algebras and representations of shifted quantum affine algebras

Related

• Quiver varieties and t-analogs of q-characters of quantum affine algebras
• An introduction to perverse sheaves
• Monoidal categories of modules over quantum affine algebras of type A and B
• Quantum cluster algebras and representations of shifted quantum affine algebras
• Modules over the small quantum group and semi-infinite flag manifold