Displaying similar documents to “Weyl algebra and a realization of the unitary symmetry”

A symplectic representation of E 7

Tevian Dray, Corinne A. Manogue, Robert A. Wilson (2014)

Commentationes Mathematicae Universitatis Carolinae

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We explicitly construct a particular real form of the Lie algebra 𝔢 7 in terms of symplectic matrices over the octonions, thus justifying the identifications 𝔢 7 ≅ 𝔰𝔭 ( 6 , 𝕆 ) and, at the group level, E 7 ≅ Sp ( 6 , 𝕆 ) . Along the way, we provide a geometric description of the minimal representation of 𝔢 7 in terms of rank 3 objects called cubies.

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

Archivum Mathematicum

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Consider a flat symplectic manifold ( M 2 l , ω ) , l ≥ 2 , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If λ is an eigenvalue of the symplectic Dirac operator such that - ı l λ is not a symplectic Killing number, then l - 1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.

Symplectic twistor operator and its solution space on ℝ 2

Marie Dostálová, Petr Somberg (2013)

Archivum Mathematicum

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We introduce the symplectic twistor operator T s in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on ℝ 2 .