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  On fundamental domains and volumes of hyperbolic Coxeter-Weyl groups

Fleig, P., Koehn, M., & Nicolai, H. (2012). On fundamental domains and volumes of hyperbolic Coxeter-Weyl groups. Letters in Mathematical Physics, 100(3), 261-278. doi:10.1007/s11005-011-0540-7.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0011-3020-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0011-3024-5
Genre: Journal Article

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1103.3175 (Preprint), 203KB
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 Creators:
Fleig, Philipp1, Author              
Koehn, Michael1, Author              
Nicolai, Hermann1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: Mathematics, Representation Theory, math.RT,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 Abstract: We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac-Moody algebras. These domains are given as subsets of certain generalized upper half planes, on which the Weyl groups act via generalized modular transformations. Our construction only requires the Cartan matrix of the underlying finite-dimensional Lie algebra and the associated Coxeter labels as input information. We present a simple formula for determining the volume of these fundamental domains. This allows us to re-produce in a simple manner the known values for these volumes previously obtained by other methods.

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 Dates: 2011-03-1620122012
 Publication Status: Published in print
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 Identifiers: arXiv: 1103.3175
DOI: 10.1007/s11005-011-0540-7
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Title: Letters in Mathematical Physics
Source Genre: Journal
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Publ. Info: Dordrecht, Holland : D. Reidel.
Pages: - Volume / Issue: 100 (3) Sequence Number: - Start / End Page: 261 - 278 Identifier: ISSN: 0377-9017
CoNE: /journals/resource/954925526816