2024/09/27 by Victor G. Kač, Minoru Wakimoto, Kac, Victor G. +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2409.18765
openalex publication_date 2024/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find modular transformations of normalized characters for the following W-algebras: (a) Wmink(\frakg), where \frakg=Dn (n ≥ 4), or E6, E7, E8, and k is a negative integer ≥ -2, or ≥ -\frach\vee6-1, respectively; (b) quantum Hamiltonian reduction of the \frakg-module L(kΛ0), where \frakg is a simple Lie algebra, f is its non-zero nilpotent element, and k is a principal admissible level with the denominator u > θ(x), where 2x is the Dynkin characteristic of f and θ is the highest root of \frakg. We prove that these vertex algebras are modular invariant. A conformal vertex algebra is called modular invariant if its character trV qL0-c/24 converges to a holomorphic modular function in the complex upper half-plane on a congruence subgroup. We find explicit formulas for their characters. Modular invariance of V is important since, in particular, conjecturally it implies that V is simple, and that V is rational, provided that it is lisse.