Charge functions for odd dimensional partitions

Abstract

To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to find the eigenvalues of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.

30 pages, 6 figures; v2: typos corrected; v3: published version

References in corpus (17)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Quantum Foam and Topological Strings
• W-symmetry, topological vertex and affine Yangian
• Crystal Melting and Toric Calabi-Yau Manifolds
• Quiver Yangian from Crystal Melting
• Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
• The Water Vapor Spectrum of APM 08279+5255: X-Ray Heating and Infrared Pumping over Hundreds of Parsecs
• Entanglement entropy and Berezin-Toeplitz operators
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Graded Quivers, Generalized Dimer Models and Toric Geometry
• Global Gluing and G-flux
• Calabi-Yau Products: Graded Quivers for General Toric Calabi-Yaus
• Charging solid partitions
• On the Classification of Duality Webs for Graded Quivers
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians