Mathematics – Quantum Algebra
Scientific paper
2008-10-30
Mathematics
Quantum Algebra
22 pages
Scientific paper
In this article, we study the Ising vectors in the vertex operator algebra $V_\Lambda^+$ associated with the Leech lattice $\Lambda$. The main result is a characterization of the Ising vectors in $V_\Lambda^+$. We show that for any Ising vector $e$ in $V_\Lambda^+$, there is a sublattice $E\cong \sqrt{2}E_8$ of $\Lambda$ such that $e\in V_E^+$. Some properties about their corresponding $\tau$-involutions in the moonshine vertex operator algebra $V^\natural$ are also discussed. We show that there is no Ising vector of $\sigma$-type in $V^\natural$. Moreover, we compute the centralizer $C_{\aut V^\natural}(z, \tau_e)$ for any Ising vector $e\in V_\Lambda^+$, where $z$ is a 2B element in $\aut V^\natural$ which fixes $V_\Lambda^+$. Based on this result, we also obtain an explanation for the 1A case of an observation by Glauberman-Norton (2001), which describes some mysterious relations between the centralizer of $z$ and some 2A elements commuting $z$ in the Monster and the Weyl groups of certain sublattices of the root lattice of type $E_8$ .
Lam Ching Hung
Shimakura Hiroki
No associations
LandOfFree
Ising vectors in the vertex operator algebra $V_Λ^+$ associated with the Leech lattice $Λ$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ising vectors in the vertex operator algebra $V_Λ^+$ associated with the Leech lattice $Λ$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ising vectors in the vertex operator algebra $V_Λ^+$ associated with the Leech lattice $Λ$ will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-278150