Adamović, Dražen; Milas, Antun The \(N=1\) triplet vertex operator superalgebras: twisted sector. (English) Zbl 1215.17018 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 087, 24 p. (2008). Summary: We classify irreducible \(\sigma \)-twisted modules for the \(N=1\) super triplet vertex operator superalgebra \(SW(m)\) introduced recently [Commun. Math. Phys. 288, No. 1, 225–270 (2009; Zbl 1235.17018)]. Irreducible graded dimensions of \(\sigma \)-twisted modules are also determined. These results, combined with our previous work in the untwisted case, show that the \(\text{SL}(2, \mathbb Z)\)-closure of the space spanned by irreducible characters, irreducible supercharacters and \(\sigma \)-twisted irreducible characters is (\(9m + 3\))-dimensional. We present strong evidence that this is also the (full) space of generalized characters for \(SW(m)\). We are also able to relate irreducible \(SW(m)\) characters to characters for the triplet vertex algebra \(W(2m + 1)\), studied in [Adv. Math. 217, 2664–2699 (2008; Zbl 1177.17017)]. Cited in 12 Documents MSC: 17B69 Vertex operators; vertex operator algebras and related structures 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B68 Virasoro and related algebras 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations Keywords:vertex operator superalgebras; Ramond twisted representations Citations:Zbl 1177.17017; Zbl 1235.17018 PDFBibTeX XMLCite \textit{D. Adamović} and \textit{A. Milas}, SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 087, 24 p. (2008; Zbl 1215.17018) Full Text: DOI arXiv EuDML