The N=1 triplet vertex operator superalgebras

Details The N=1 triplet vertex operator superalgebras The N=1 triplet vertex operator superalgebras

2007-12-03

arxiv.org/abs/0712.0379v4

Commun.Math.Phys.288:225-270,2009

Mathematics

Quantum Algebra

53 pages; v2: references added; v3: a few changes; v4: final version, to appear in CMP

Scientific paper

10.1007/s00220-009-0735-2

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We classify irreducible SW(m)-modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible SW(m) characters. Finally, we contemplate possible connections between the category of SW(m)-modules and the category of modules for the quantum group U^{small}_q(sl_2), q=e^{\frac{2 \pi i}{2m+1}}, by focusing primarily on properties of characters and the Zhu's algebra A(SW(m)). This paper is a continuation of arXiv:0707.1857.

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