Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Compact Lie groups: Euler constructions and generalized Dyson conjecture


Authors: S. L. Cacciatori, F. Dalla Piazza and A. Scotti
Journal: Trans. Amer. Math. Soc. 369 (2017), 4709-4724
MSC (2010): Primary 22C05, 22E15, 22E46
DOI: https://doi.org/10.1090/tran/6795
Published electronically: January 9, 2017
MathSciNet review: 3632547
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A generalized Euler parameterization of a compact Lie group is a way for parameterizing the group starting from a maximal Lie subgroup, which allows a simple characterization of the range of parameters. In the present paper we consider the class of all compact connected Lie groups. We present a general method for realizing their generalized Euler parameterization starting from any symmetrically embedded Lie group. Our construction is based on a detailed analysis of the geometry of these groups. As a byproduct this gives rise to an interesting connection with certain Dyson integrals. In particular, we obtain a geometry based proof of a Macdonald conjecture regarding the Dyson integrals correspondent to the root systems associated to all irreducible symmetric spaces. As an application of our general method we explicitly parameterize all groups of the class of simple, simply connected compact Lie groups. We provide a table giving all necessary ingredients for all such Euler parameterizations.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 22C05, 22E15, 22E46

Retrieve articles in all journals with MSC (2010): 22C05, 22E15, 22E46


Additional Information

S. L. Cacciatori
Affiliation: Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, Via Valleggio 11, 22100 Como, Italy – and – INFN, via Celoria 16, 20133 Milano, Italy
Email: sergio.cacciatori@uninsubria.it

F. Dalla Piazza
Affiliation: Dipartimento di Matematica, Università “La Sapienza”, Piazzale A. Moro 2, I-00185, Roma, Italy
Email: f.dallapiazza@gmail.com

A. Scotti
Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
Email: antonio.scotti@gmail.com

DOI: https://doi.org/10.1090/tran/6795
Keywords: Lie groups, Euler parameterization, Macdonald conjecture, Dyson integral
Received by editor(s): May 19, 2014
Received by editor(s) in revised form: June 22, 2015, June 25, 2015, and July 20, 2015
Published electronically: January 9, 2017
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society