Virasoro constraints and representations for quiver moduli spaces

2024/03/20 by Woonam Lim, Lim, Woonam, Miguel Moreira +1
Mathematics · Computer Science · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2403.13982

Abstract

We study the Virasoro constraints for moduli spaces of representations of quiver with relations by Joyce's vertex algebras. Using the framed Virasoro constraints, we construct a representation of half of the Virasoro algebra on the cohomology of moduli stacks of quiver representations under smoothness assumption. By exploiting the non-commutative nature of the Virasoro operators, we apply our theory for quivers to del Pezzo surfaces using exceptional collections. In particular, the Virasoro constraints and representations are proven for moduli of sheaves on ℙ², ℙ¹× ℙ¹ and Bl_pt(ℙ²). Lastly, we unravel the Virasoro constraints for Grassmannians in terms of symmetric polynomials and Hecke operators.

Related

• Universal Virasoro constraints for quivers with relations
• Virasoro constraints on moduli of sheaves and vertex algebras
• Lecture Notes on Quiver Representations and Moduli Problems in Algebraic Geometry
• Virasoro constraints for moduli spaces of sheaves on surfaces
• Moduli of representations of quivers