Journal of Generalized Lie Theory and Applications

Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization

A Caine and D Pickrell

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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.

Article information

Source
J. Gen. Lie Theory Appl., Volume 9, Number 2 (2015), 14 pages.

Dates
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1454422007

Digital Object Identifier
doi:10.4172/1736-4337.1000233

Mathematical Reviews number (MathSciNet)
MR3642244

Zentralblatt MATH identifier
06538944

Keywords
Noncompact groups Birkhoff factorization Weyl group

Citation

Caine, A; Pickrell, D. Loops in Noncompact Groups of Hermitian Symmetric Type and Factorization. J. Gen. Lie Theory Appl. 9 (2015), no. 2, 14 pages. doi:10.4172/1736-4337.1000233. https://projecteuclid.org/euclid.jglta/1454422007


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