Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 087, 24 pages      arXiv:0806.3560
Contribution to the Special Issue on Kac-Moody Algebras and Applications

The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector

Drazen Adamovic a and Antun Milas b
a) Department of Mathematics, University of Zagreb, Croatia
b) Department of Mathematics and Statistics, University at Albany (SUNY), Albany, NY 12222, USA

Received August 31, 2008, in final form December 05, 2008; Published online December 13, 2008

We classify irreducible σ-twisted modules for the N = 1 super triplet vertex operator superalgebra SW(m) introduced recently [Adamovic D., Milas A., Comm. Math. Phys., to appear, arXiv:0712.0379]. Irreducible graded dimensions of σ-twisted modules are also determined. These results, combined with our previous work in the untwisted case, show that the SL(2,Z)-closure of the space spanned by irreducible characters, irreducible supercharacters and σ-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 [Adamovic D., Milas A., Adv. Math. 217 (2008), 2664-2699, arXiv:0707.1857].

Key words: vertex operator superalgebras; Ramond twisted representations.

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