Presentations of Principal Subspaces of Higher Level Standard A2(2)-Modules

We study the principal subspaces of higher level standard A 2 ( 2 ) -modules, extending earlier work in the level one case, by Calinescu, Lepowsky and Milas. We prove natural presentations of principal subspaces and also of certain related spaces. By using these presentations we obtain exact sequenc...

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Bibliographic Details
Published in:Algebras and representation theory 2019-12, Vol.22 (6), p.1457-1478
Main Authors: Calinescu, Corina, Penn, Michael, Sadowski, Christopher
Format: Article
Language:English
Subjects:
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
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Summary:We study the principal subspaces of higher level standard A 2 ( 2 ) -modules, extending earlier work in the level one case, by Calinescu, Lepowsky and Milas. We prove natural presentations of principal subspaces and also of certain related spaces. By using these presentations we obtain exact sequences, which yield recursions satisfied by the characters of the principal subspaces and related spaces. We conjecture a formula for a specialized character of the principal subspace, given by the Nahm sum of the inverse of the tadpole Cartan matrix.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-018-9828-y