A Kac-Moody algebra associated to the non-compact manifold SL$(2, \mathbb R)$

Rutwig Campoamor-Strusberg; Alessio Marrani; Michel Rausch de Traubenberg

A Kac-Moody algebra associated to the non-compact manifold SL$(2, \mathbb R)$

Mathematical Physics 2024-09-25 v1 High Energy Physics - Theory math.MP Representation Theory

Authors: Rutwig Campoamor-Strusberg , Alessio Marrani , Michel Rausch de Traubenberg

Abstract

We construct explicitly a Kac-Moody algebra associated to SL $(2, \mathbb R)$ in two different but equivalent ways: either by identifying a Hilbert basis of $L^2($ SL $(2, \mathbb R))$ or by the Plancherel Theorem. Central extensions and Hermitean differential operators are identified.

Keywords

Kac-Moody algebra SL$(2, \mathbb R)$ Hilbert basis Plancherel Theorem central extension

Cite

@article{arxiv.2409.15837,
  title  = {A Kac-Moody algebra associated to the non-compact manifold SL$(2, \mathbb R)$},
  author = {Rutwig Campoamor-Strusberg and Alessio Marrani and Michel Rausch de Traubenberg},
  journal= {arXiv preprint arXiv:2409.15837},
  year   = {2024}
}

Comments

16 pages, no figures, contribution to GROUP33/35 held in Cotonou, Benin, July 15 - 19, 2024

A Kac-Moody algebra associated to the non-compact manifold SL$(2, \mathbb R)$

Abstract

Keywords

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