Quiver W-algebras

2015/12/31 by Taro Kimura, Vasily Pestun · 78 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Centralizer and normalizer #Formalism (music) #Fundamental representation #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Quantum field theory #Quiver #Representation (politics) #Representation theory #hep-th #math.AG #math.KT #math.RT

paper · pdf · doi:10.1007/s11005-018-1072-1

published in Letters in Mathematical Physics 108(6), 1351-1381 (Springer Science+Business Media) · 26 pages; typo corrected, ref. added; minor changes, published version

openalex created_date 2016/06/24 · arxiv created 2018/03/20 · openalex publication_date 2018/03/21 · arxiv updated 2018/05/08 · openalex updated_date 2026/08/06

Abstract

For a quiver with weighted arrows we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al., and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

Citations

• Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
• Quiver varieties and finite dimensional representations of quantum affine algebras
• Hall algebras and quantum groups
• Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1
• Gauge invariant matrix model for the Â-D-Ê closed strings
• Matrix models for β-ensembles from Nekrasov partition functions
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Electric-magnetic duality and the geometric Langlands program
• A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

Cited by

• Quiver elliptic W-algebras
• Quiver BPS Indices from Crystal Profiles
• Fractional quiver W-algebras
• Twisted reduction of quiver W-algebras

Related

• Quiver elliptic W-algebras
• Twisted reduction of quiver W-algebras
• K-theoretic Hall algebras for quivers with potential
• Quiver algebras and their representations for arbitrary quivers
• Introduction to quiver varieties -- for ring and representation theoriests