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The $N=1$ Triplet Vertex Operator Superalgebras: Twisted Sector
Drazen Adamovica,
Antun Milasb a Department of Mathematics, University of Zagreb, Croatia
b Department of Mathematics and Statistics, University at Albany (SUNY), Albany, NY 12222, USA
Abstract:
We classify irreducible
$\sigma$-twisted modules for the
$N=1$ super triplet vertex operator superalgebra
$\mathcal{SW}(m)$ introduced recently [Adamović D., Milas A.,
Comm. Math. Phys., to appear,
arXiv:0712.0379]. Irreducible graded dimensions of
$\sigma$-twisted modules are also determined. These results, combined with our previous work in the untwisted case, show that the
$SL(2,\mathbb Z)$-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
$\mathcal{SW}(m)$. We are also able to relate irreducible
$\mathcal{SW}(m)$ characters to characters for the triplet vertex algebra
$\mathcal W(2m+1)$, studied in
[Adamović D., Milas A.,
Adv. Math. 217 (2008), 2664–2699,
arXiv:0707.1857].
Keywords:
vertex operator superalgebras; Ramond twisted representations.
MSC: 17B69;
17B67;
17B68;
81R10 Received: August 31, 2008; in final form
December 5, 2008; Published online
December 13, 2008
Language: English
DOI:
10.3842/SIGMA.2008.087
Fulltext:
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