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
Abstract

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

Keywords
Takiff Lie algebras, symmetric invariants, Jacobian, Harish-Chandra projection
Mathematical Subject Classification 2010
Primary: 17B20, 17B35, 17B70
Secondary: 22E47