Open Access
2015 Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization
A Caine, D Pickrell
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J. Gen. Lie Theory Appl. 9(2): 1-14 (2015). DOI: 10.4172/1736-4337.1000233
Abstract

In studies of Pittmann, 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 semisimple Lie group of Hermitian symmetric type. In literature of caine, we showed that for an element of, i.e. a constant loop, there is a unique Birkhoff factorization if and only if there is a root subgroup factorization. However for loops in, 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.

Copyright © 2015 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)
A Caine and D Pickrell "Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization," Journal of Generalized Lie Theory and Applications 9(2), 1-14, (2015). https://doi.org/10.4172/1736-4337.1000233
Published: 2015
Vol.9 • No. 2 • 2015
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