Related papers: The Model Of Paths For Generalized Kac-Moody Algeb…
This manuscript has been withdrawn by the author. Some of the material has been included in the manuscript 'Dualizing the Dual Standard Model' hep-ph/0102084.
This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.
This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).
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There is a technical issue in the analysis that is not easily fixable. We, therefore, withdraw the submission. Sorry for the inconvenience.
We show that Joseph-Lamprou's path model for representations of generalized Kac-Moody algebras can be embedded into Littelmann's path model for certain Kac-Moody algebras. Using this embedding, for Joseph-Lamprou's path crystals, we give a…
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This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.
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This preprint has been withdrawn. It is because I will never publish this preprint since everything has been contained in my new preprint: arXiv:0907.1506. Please refer to arXiv:0907.1506. Please do not cite this preprint any more.
This paper has been withdrawn by the authors due to the existence of main results in the literature.