Segal's contractions, AdS and conformal groups
Abstract
Symmetries and their applications always played an important role in I.E. Segal's work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the ``O'Raifeartaigh theorem", continuing with his incidental introduction in 1951 of the (1953) InönüWigner contractions, of which the passage from AdS (SO(2,3)) to Poincaré is an important example, and with his interest in conformal groups in the latter part of last century. Since the 60s Flato and I had many fruitful interactions with him around these topics. In a last section I succinctly relate these interests in symmetries with several of ours, especially elementary particles symmetries and deformation quantization, and with an ongoing program combining both.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2212.14316
 arXiv:
 arXiv:2212.14316
 Bibcode:
 2022arXiv221214316S
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Group Theory;
 Mathematics  Quantum Algebra;
 70S10 (Primary);
 53D55;
 17B37;
 20G42;
 81T20;
 81V25;
 83C47 (Secondary)
 EPrint:
 12 pages, invited talk at Group32 (Prague 2018), to be published in the Proceedings of Group34 (Strasbourg 2022), minor modifications to the 2018 Group32 text to adapt it to the SciPost style