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Two moonshines for L2(11) but none for M12
, Sutapa Samanta
Published in Elsevier B.V.
2019
Volume: 939
   
Pages: 566 - 598
Abstract
In this paper, we revisit an earlier conjecture by one of us that related conjugacy classes of M12 to Jacobi forms of weight zero and index one. We construct Jacobi forms for all conjugacy classes of M12 that are consistent with constraints from group theory as well as modularity. However, we obtain 1427 solutions that satisfy these constraints (to the order that we checked) and are unable to provide a unique Jacobi form. Nevertheless, as a consequence, we are able to provide a group theoretic proof of the evenness of the coefficients of all EOT Jacobi forms associated with conjugacy classes of M12:2⊂M24. We show that there exists no solution where the Jacobi forms (for order 4/8 elements of M12) transform with phases under the appropriate level. In the absence of a moonshine for M12, we show that there exist moonshines for two distinct L2(11) sub-groups of the M12. We construct Siegel modular forms for all L2(11) conjugacy classes and show that each of them arises as the denominator formula for a distinct Borcherds–Kac–Moody Lie superalgebra. © 2019
About the journal
JournalData powered by TypesetNuclear Physics B
PublisherData powered by TypesetElsevier B.V.
ISSN05503213
Open AccessNo