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

Oksana Yakimova

Vol. 306 (2020), No. 1, 375–383

DOI: 10.2140/pjm.2020.306.375

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 $\mathcal{𝒵}\left(\mathfrak{𝔤}\right)\subset \mathcal{𝒰}\left(\mathfrak{𝔤}\right)$. 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

Milestones

Received: 7 December 2018

Revised: 13 December 2019

Accepted: 2 January 2020

Published: 14 June 2020