## African Diaspora Journal of Mathematics

- Afr. Diaspora J. Math. (N.S.)
- Volume 18, Number 2 (2015), 1-10.

### On Irreducibility of an Induced Representation of a Simply Connected Nilpotent Lie Group

Adjiey Jean-Luc Koffi and Kinvi Kangni

#### Abstract

Let $G$ be a simply connected nilpotent Lie group, $\mathcal{G}$ the finite-dimensional Lie algebra of $G$, $\mathcal{V}$ a finite-dimensional vector space over $\mathbb{C}$ or $\mathbb{R}$, and $H$ a connected Lie subgroup of $G$ such that the Lie algebra of $H$ is a subordinate subalgebra to an element $\pi $ of $Hom\left( \mathcal{G},gl\left( \mathcal{V}\right) \right) $. In this work, we construct an irreducible representation $\chi _{\pi }$ of $H$ such that the induced of $ \chi _{\pi }$ on $G$ is irreducible.

#### Article information

**Source**

Afr. Diaspora J. Math. (N.S.), Volume 18, Number 2 (2015), 1-10.

**Dates**

First available in Project Euclid: 2 November 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.adjm/1446472393

**Mathematical Reviews number (MathSciNet)**

MR3400324

**Zentralblatt MATH identifier**

1343.22007

**Keywords**

Polarization at an operator subordinate subalgebra to an operator induced representation

#### Citation

Koffi, Adjiey Jean-Luc; Kangni, Kinvi. On Irreducibility of an Induced Representation of a Simply Connected Nilpotent Lie Group. Afr. Diaspora J. Math. (N.S.) 18 (2015), no. 2, 1--10. https://projecteuclid.org/euclid.adjm/1446472393