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  Decompositions of hyperbolic Kac-Moody algebras with respect to imaginary root groups

Feingold, A. J., Kleinschmidt, A., & Nicolai, H. (2024). Decompositions of hyperbolic Kac-Moody algebras with respect to imaginary root groups. Communications in Mathematical Physics, 405(10): 241. doi:10.1007/s00220-024-05107-2.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000F-6F25-C Version Permalink: https://hdl.handle.net/21.11116/0000-000F-DB4A-8
Genre: Journal Article

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 Creators:
Feingold, Alex J., Author
Kleinschmidt, Axel1, Author           
Nicolai, Hermann2, Author           
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Quantum 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,High Energy Physics - Theory, hep-th
 Abstract: We propose a novel way to define imaginary root subgroups associated with
(timelike) imaginary roots of hyperbolic Kac-Moody algebras. Using in an
essential way the theory of unitary irreducible representation of covers of the
group SO(2,1), these imaginary root subgroups act on the complex Kac-Moody
algebra viewed as a Hilbert space. We illustrate our new view on Kac-Moody
groups by considering the example of a rank-two hyperbolic algebra that is
related to the Fibonacci numbers. We also point out some open issues and new
avenues for further research, and briefly discuss the potential relevance of
the present results for physics and current attempts at unification.

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 Dates: 2024-02-272024
 Publication Status: Issued
 Pages: 42 pages, 4 figures
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 Rev. Type: -
 Identifiers: arXiv: 2402.17737
DOI: 10.1007/s00220-024-05107-2
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 405 (10) Sequence Number: 241 Start / End Page: - Identifier: -