Vol. 306, No. 1, 2020

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A combinatorial identity for the Jacobian of $t$-shifted invariants

Oksana Yakimova

Vol. 306 (2020), No. 1, 375–383

Let 𝔤 be a simple Lie algebra. There are classical formulas for the Jacobians of the generating invariants of the Weyl group of 𝔤 and of the images under the Harish-Chandra projection of the generators of the centre 𝒵(𝔤) 𝒰(𝔤). We present a modification of these formulas related to Takiff Lie algebras.

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Takiff Lie algebras, symmetric invariants, Jacobian, Harish-Chandra projection
Mathematical Subject Classification 2010
Primary: 17B20, 17B35, 17B70
Secondary: 22E47
Received: 7 December 2018
Revised: 13 December 2019
Accepted: 2 January 2020
Published: 14 June 2020
Oksana Yakimova
Universität zu Köln, Mathematisches Institut
Institut für Mathematik
Friedrich Schiller Universität Jena