Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by \mathfraksl₂ subalgebras which are generalizations of principal \mathfraksl₂ subalgebras

2023/01/02 by Hisanori Tsurusaki, Tsurusaki, Hisanori
Mathematics · Physics and Astronomy · #17B67 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2301.00522

openalex publication_date 2023/01/02 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

Abstract

There exist principal \mathfraksl₂ subalgebras for hyperbolic Kac-Moody Lie algebras. In the case of rank 2 symmetric hyperbolic Kac-Moody Lie algebras, certain \mathfraksl₂ subalgebras are constructed. These subalgebras are generalizations of principal \mathfraksl₂ subalgebras. We show that the rank 2 symmetric hyperbolic Kac-Moody Lie algebras themselves are irreducibly decomposed under the action of this \mathfraksl₂ subalgebras. Furthermore, we classify irreducible components of the decomposition. In particular, we obtain multiplicities of unitary principal series and complementary series.

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