Recursive multigraph-based constructions produce families of generalized Cartan matrices with exponentially growing coranks for Kac-Moody algebras, with explicit spectra computed via adjacency eigenvalue multiplicity.
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We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.
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A method constructs closed string trajectories from open string seeds dressed by symplectic algebra generators via Howe duality, with physical states identified by solving Diophantine recursion relations.
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On a new class of high-corank Kac-Moody algebras
Recursive multigraph-based constructions produce families of generalized Cartan matrices with exponentially growing coranks for Kac-Moody algebras, with explicit spectra computed via adjacency eigenvalue multiplicity.