Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization
Caine A* and Pickrell D
California State Polytechnic University Pomona, Mathematics and Statistics, 3801 W, Temple Ave. Pomona, CA 91768, USA
- Corresponding Author:
- Caine A
Professor, California State Polytechnic University Pomona
Mathematics and Statistics, 3801 W
Temple Ave. Pomona, CA 91768, USA
E-mail: [email protected]
Received date: July 29, 2015 Accepted date: October 30, 2015 Published date: November 05, 2015
Citation: Caine A, Pickrell D (2015) Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization. J Generalized Lie Theory Appl 9:233. doi: 10.4172/1736-4337.1000233
Copyright: © 2015 Caine A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In previous work with Pittmann-Polletta, we showed that a loop in a simply connected compact Lie group has a unique Birkhoff (or triangular) factorization if and only if the loop has a unique root subgroup factorization (relative to a choice of a reduced sequence of simple reflections in the affine Weyl group). In this paper our main purpose is to investigate Birkhoff and root subgroup factorization for loops in a noncompact type semisimple Lie group of Hermitian symmetric type. In previous work we showed that for a constant loop there is a unique Birkhoff factorization if and only if there is a root subgroup factorization. However for loops, while a root subgroup factorization implies a unique Birkhoff factorization, the converse is false. As in the compact case, root subgroup factorization is intimately related to factorization of Toeplitz determinants.