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## Contravariant form for reduction algebras

Journal of Geometry and Physics. 2018. Vol. 129. P. 99-116.
Khoroshkin S. M., Ogievetsky O.

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 specializations 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 gln with a symmetric or wedge tensor power of its fundamental representation.