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A Geometric Realization of $s l (6, ℂ)$

Giovanni Gaiffi; Michele Grassi — 2009

Rendiconti del Seminario Matematico della Università di Padova

Lie Algebra bundles on s-Kähler manifolds, with applications to Abelian varieties

Giovanni Gaiffi; Michele Grassi — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that one can obtain natural bundles of Lie algebras on rank two $s$ -Kähler manifolds, whose fibres are isomorphic respectively to $so (s + 1, s + 1)$ , $su (s + 1, s + 1)$ and $sl (2 s + 2, ℝ)$ . These bundles have natural flat connections, whose flat global sections generalize the Lefschetz operators of Kähler geometry and act naturally on cohomology. As a first application, we build an irreducible representation of a rational form of $su (s + 1, s + 1)$ on (rational) Hodge classes of Abelian varieties with rational period matrix.

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A Geometric Realization of s l ( 6 , ℂ )

Lie Algebra bundles on s-Kähler manifolds, with applications to Abelian varieties

A Geometric Realization of $s l (6, ℂ)$