Weierstrass sections for some truncated parabolic subalgebras

JOURNAL OF ALGEBRA

卷:580

Article

Fauquant-Millet, Florence¹ 

[1] Univ Lyon, Inst Camille Jordan, UJM St Etienne, CNRS UMR 5208, F-42023 St Etienne, France

关键词: Weierstrass section;    Adapted pair;    Slice;    Parabolic subalgebra;    Polynomiality;    Symmetric invariants;    Semi-invariants;   

DOI  :  10.1016/j.jalgebra.2021.03.033

来源: Elsevier

【 摘 要 】

In this paper, using Bourbaki's convention, we consider a simple Lie algebra g subset of gl(m) of type B, C or D and a parabolic subalgebra p of g associated with a Levi factor composed essentially, on each side of the second diagonal, by successive blocks of size two, except possibly for the first and the last ones. Extending the notion of a Weierstrass section introduced by Popov to the coadjoint action of the truncated parabolic subalgebra associated with p, we construct explicitly Weierstrass sections, which give the polynomiality (when it was not yet known) for the algebra generated by semi-invariant polynomial functions on the dual space p* of p and which allow to linearize semi-invariant generators. Our Weierstrass sections require the construction of an adapted pair, which is the analogue of a principal sl(2)-triple in the non reductive case. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free