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SIGMA 4 (2008), 087, 24 pages arXiv:0806.3560
https://doi.org/10.3842/SIGMA.2008.087
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
Abstract
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.
pdf (362 kb)
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