On exceptional vertex operator (Super) algebras
View/Open
Date
20141001Author
Tuite, Michael P.
Van, Hoang Dinh
Metadata
Show full item recordUsage
This item's downloads: 135 (view details)
Cited 4 times in Scopus (view citations)
Recommended Citation
Tuite M.P., Van H.D. (2014) On Exceptional Vertex Operator (Super) Algebras. In: Mason G., Penkov I., Wolf J. (eds) Developments and Retrospectives in Lie Theory. Developments in Mathematics, vol 38. Springer, Cham
Published Version
Abstract
We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generate the algebra. We also discuss conditions on the reducibility of the lowest weight primary vectors as a module for the automorphism group. Finally we analyse solutions for exceptional vertex operator algebras with primary vectors of lowest weight up to 9 and for vertex operator superalgebras with primary vectors of lowest weight up to 17/2. Most solutions can be identified with simple ordinary modules for known algebras but there are also four conjectured algebras generated by weight two primaries and three conjectured extremal vertex operator algebras generated by primaries of weight 3, 4 and 6 respectively.
Collections
This item is available under the AttributionNonCommercialNoDerivs 3.0 Ireland. No item may be reproduced for commercial purposes. Please refer to the publisher's URL where this is made available, or to notes contained in the item itself. Other terms may apply.
The following license files are associated with this item:
Related items
Showing items related by title, author, creator and subject.

N = 2 and n = 4 subalgebras of super vertex operator algebras
Mason, Geoffrey; Tuite, Michael; Yamskulna, Gaywalee (IOP Publishing, 20180112)We develop criteria to decide if an N = 2 or N = 4 superconformal algebra is a subalgebra of a super vertex operator algebra in general, and of a super lattice theory in particular. We give some specific examples. 
Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
Bishop, Marcus; Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Elsevier, 20141106)In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the pth graded ... 
On the Torus degeneration of the genus two partition function
Hurley, Donny; Tuite, Michael P. (World Scientific Publishing, 20130716)We consider the partition function of a general vertex operator algebra V on a genus two Riemann surface formed by sewing together two tori. We consider the nontrivial degeneration limit where one torus is pinched down ...