Row and column detection complexities of character tables

Abstract

Character tables of finite groups and closely related commutative algebras have been investigated recently using new perspectives arising from the AdS/CFT correspondence and low-dimensional topological quantum field theories. Two important elements in these new perspectives are physically motivated definitions of quantum complexity for the algebras and a notion of row-column duality. These elements are encoded in properties of the character table of a group G and the associated algebras, notably the centre of the group algebra and the fusion algebra of irreducible representations of the group. Motivated by these developments, we define row and column versions of detection complexities for character tables, and investigate the relation between these complexities under the exchange of rows and columns. We observe regularities that arise in the statistical averages over small character tables and propose corresponding conjectures for arbitrarily large character tables.

35 pages, 4 figures, 2 tables

References in corpus (23)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Bubbling AdS space and 1/2 BPS geometries
• Machine Learning in the String Landscape
• Machine Learning of Calabi-Yau Volumes
• Deep Learning and AdS/CFT
• Evolving neural networks with genetic algorithms to study the String Landscape
• Machine Learning CICY Threefolds
• Neural Networks and Quantum Field Theory
• Machine learning Calabi-Yau metrics
• Integrability vs. Information Loss: A Simple Example
• Deep Learning the Hyperbolic Volume of a Knot
• Machine Learning Line Bundle Cohomology
• BPS states, conserved charges and centres of symmetric group algebras
• Combinatoric topological string theories and group theory algorithms
• Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
• Integrality, Duality and Finiteness in Combinatoric Topological Strings
• The quantum detection of projectors in finite-dimensional algebras and holography
• Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds
• Learning BPS Spectra and the Gap Conjecture
• Two-dimensional gauge theories of the symmetric group S(n) and branched n-coverings of Riemann surfaces in the large-n limit
• Row-Column duality and combinatorial topological strings
• Kronecker coefficients from algebras of bi-partite ribbon graphs