0-affine quantum groups as K-theoretic Hall algebras

2025/12/09 by Hsu, You-Hung
Mathematics · #18G80 #19L47 #20G42 : Secondary 14F08 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 17B37 #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.08272

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

In this note, we show that the positive part of Arkhipov-Mazin's 0-affine quantum group can be realized as the K-theoretic Hall algebra of the type A Dynkin quiver. We then construct a categorical action of this positive part and demonstrate that such an action induces semiorthogonal decompositions on the corresponding weight categories. As a main example, we study the bounded derived category of coherent sheaves on n-step partial flag varieties.

Citations

• Cohomological Hall algebras of quivers and Yangians
• Okounkov's conjecture via BPS Lie algebras
• Categorical idempotents via shifted 0-affine algebras
• Semiorthogonal decomposition via categorical action
• Generators for K-theoretic Hall algebras of quivers with potential
• Categorical and K-theoretic Hall algebras for quivers with potential
• K-theoretic Hall algebras of quivers with potential as Hopf algebras
• K-theoretic Hall algebras, quantum groups and super quantum groups
• A categorical action of the shifted q=0 affine algebra
• On cohomological Hall algebras of quivers : generators
• Idempotents in triangulated monoidal categories
• Quantum difference equation for Nakajima varieties
• The integrality conjecture and the cohomology of preprojective stacks
• Quantum Algebras and Cyclic Quiver Varieties
• On the Cohomological Hall Algebra of Dynkin quivers
• Quantum Groups and Quantum Cohomology
• The Shuffle Algebra Revisited
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Lectures on Hall algebras
• Quiver Varieties and Yangians
• Quiver varieties and finite dimensional representations of quantum affine algebras
• Affine quantum groups and equivariant K-theory

Related

• K-theoretic Hall algebras, quantum groups and super quantum groups
• A categorical action of the shifted q=0 affine algebra
• Hall algebras and shifted quantum affine algebras
• Generators for K-theoretic Hall algebras of quivers with potential
• Sheaf realization of Bridgeland's Hall algebra of Dynkin type