Contravariant form for reduction algebras

JOURNAL OF GEOMETRY AND PHYSICS

卷:129

Article

Khoroshkin, S.^1,2  Ogievetsky, O.^3,4 

[1] ITEP, B Cheremushkinskaya 25, Moscow 117218, Russia

[2] Natl Res Univ, Higher Sch Econ, Myasnitskaya 20, Moscow 101000, Russia

[3] Univ Toulon & Var, Aix Marseille Univ, CNRS, CPT, Marseille, France

[4] Kazan Fed Univ, Kremlevskaya 17, Kazan 420008, Russia

关键词: Reduction algebra;    Contravariant form;    Shapovalov form;    Harish-Chandra map;    Deformations of rings of differential operators;    Singular vectors;   

DOI  :  10.1016/j.geomphys.2018.03.001

来源: Elsevier

【 摘 要 】

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 gl(n) with a symmetric or wedge tensor power of its fundamental representation. (c) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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