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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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

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

First available in Project Euclid: 2 February 2016

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Noncompact groups Birkhoff factorization Weyl group


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.

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