sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras

We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras. These Lie superalgebras have a sl(2)ˆ subalgebra which we use...

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Autores principales:	Suresh Govindarajan, Mohammad Shabbir, Sankaran Viswanath
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/0db7df3b19bc45c08c35a38ab69f44ba
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spelling	oai:doaj.org-article:0db7df3b19bc45c08c35a38ab69f44ba2021-12-04T04:33:02Zsl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras0550-321310.1016/j.nuclphysb.2021.115614https://doaj.org/article/0db7df3b19bc45c08c35a38ab69f44ba2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0550321321003114https://doaj.org/toc/0550-3213We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras. These Lie superalgebras have a sl(2)ˆ subalgebra which we use to study the Siegel modular forms. We show that the expansion of the Umbral Jacobi forms in terms of sl(2)ˆ characters leads to vector-valued modular forms. We obtain closed formulae for these vector-valued modular forms. In the Lie algebraic context, the Fourier coefficients of these vector-valued modular forms are related to multiplicities of roots appearing on the sum side of the Weyl-Kac-Borcherds denominator formulae.Suresh GovindarajanMohammad ShabbirSankaran ViswanathElsevierarticleNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENNuclear Physics B, Vol 973, Iss , Pp 115614- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Suresh Govindarajan Mohammad Shabbir Sankaran Viswanath sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
description	We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras. These Lie superalgebras have a sl(2)ˆ subalgebra which we use to study the Siegel modular forms. We show that the expansion of the Umbral Jacobi forms in terms of sl(2)ˆ characters leads to vector-valued modular forms. We obtain closed formulae for these vector-valued modular forms. In the Lie algebraic context, the Fourier coefficients of these vector-valued modular forms are related to multiplicities of roots appearing on the sum side of the Weyl-Kac-Borcherds denominator formulae.
format	article
author	Suresh Govindarajan Mohammad Shabbir Sankaran Viswanath
author_facet	Suresh Govindarajan Mohammad Shabbir Sankaran Viswanath
author_sort	Suresh Govindarajan
title	sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
title_short	sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
title_full	sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
title_fullStr	sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
title_full_unstemmed	sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras
title_sort	sl(2)ˆ decomposition of denominator formulae of some bkm lie superalgebras
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/0db7df3b19bc45c08c35a38ab69f44ba
work_keys_str_mv	AT sureshgovindarajan sl2ˆdecompositionofdenominatorformulaeofsomebkmliesuperalgebras AT mohammadshabbir sl2ˆdecompositionofdenominatorformulaeofsomebkmliesuperalgebras AT sankaranviswanath sl2ˆdecompositionofdenominatorformulaeofsomebkmliesuperalgebras
_version_	1718373012791623680

sl(2)ˆ decomposition of denominator formulae of some BKM Lie superalgebras

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