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Article Dans Une Revue Journal of Geometry and Physics Année : 2018

Contravariant form for reduction algebras

Résumé

We define contravariant forms on diagonal reduction algebras, algebras of h-deformed differential operators and on standard modules over these algebras. We study properties of these forms and their specializations. We show that the special-izations of the forms on the spaces of h-commuting variables present zero singular vectors iff they are in the kernel of the specialized form. As an application we compute norms of highest weight vectors in the tensor product of an irreducible finite dimensional representation of the Lie algebra gl n with a symmetric or wedge tensor power of its fundamental representation.
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Dates et versions

hal-01259064 , version 1 (11-05-2018)

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S. Khoroshkin, O. Ogievetsky. Contravariant form for reduction algebras. Journal of Geometry and Physics, 2018, 129, pp.99-116. ⟨10.1016/j.geomphys.2018.03.001⟩. ⟨hal-01259064⟩
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