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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


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.


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A Caine. D Pickrell. "Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization." J. Gen. Lie Theory Appl. 9 (2) 1 - 14, 2015.


Published: 2015
First available in Project Euclid: 2 February 2016

zbMATH: 06538944
MathSciNet: MR3642244
Digital Object Identifier: 10.4172/1736-4337.1000233

Keywords: Birkhoff factorization , Noncompact groups , Weyl group

Rights: Copyright © 2015 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.9 • No. 2 • 2015
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