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Classification of Simple Cuspidal Modules Over a Lattice Lie Algebra of Witt Type

Published online by Cambridge University Press:  13 January 2020

Y. Billig
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Canada Email: billig@math.carleton.ca
K. Iohara
Affiliation:
Université Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France Email: iohara@math.univ-lyon1.fr

Abstract

Let $W_{\unicode[STIX]{x1D70B}}$ be the lattice Lie algebra of Witt type associated with an additive inclusion $\unicode[STIX]{x1D70B}:\mathbb{Z}^{N}{\hookrightarrow}\mathbb{C}^{2}$ with $N>1$. In this article, the classification of simple $\mathbb{Z}^{N}$-graded $W_{\unicode[STIX]{x1D70B}}$-modules, whose multiplicities are uniformly bounded, is given.

Type
Article
Copyright
© Canadian Mathematical Society 2020

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Footnotes

The first author gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada. The second author is partially supported by the French ANR (ANR project ANR-15-CE40-0012). He would like to also thank the Embassy of France in Canada for the mobility grant that allowed him to visit Carleton University. This work was partially supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon. We would also like to thank the University of Lyon and Carleton University for the hospitality during our respective visits.

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