2018/05/24 by Dražen Adamović, Adamovic, Drazen, Antun Milas +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1805.09771
openalex publication_date 2018/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We consider several vertex operator (super)algebras closely related to\nV-1( fraksl (n) ), n \≥ 3 : (a) the parafermionic subalgebra\nK( fraksl(n),-1) for which we completely describe its inner structure, (b)\nthe vacuum algebra \Ω (V-1( fraksl (n) ) ), and (c) an infinite\nextension mathcal U of V-1( fraksl (n) ) constructed by combining\ncertain irreducible ordinary modules with integral weights. It turns out that\n mathcal U is isomorphic to the coset vertex algebra frakpsl(n|n) 1 /\n fraksl(n)1, n \≥ 3. We show that V-1( fraksl(n)) admits\nprecisely n ordinary irreducible modules, up to isomorphism. This leads to\nthe conjecture that mathcal U is em quasi-lisse. We present evidence in\nsupport of this conjecture: we prove that the (super)character of mathcal U\nis quasi-modular of weight one by virtue of being the constant term of a\nmeromorphic Jacobi form of index zero. Explicit formulas and MLDE for\ncharacters and supercharacters are given for frakg= fraksl(3) and\noutlined for general n. We present a conjectural family of 2nd order MLDEs\nfor characters of vertex algebras frakpsl(n|n) 1, n \≥ 2. We finish\nwith a theorem pertaining to characters of frakpsl(n|n)1 and mathcal\nU-modules.\n