A Note on Iwasawa-Type Decomposition
We study the Iwasawa-type decomposition of an open subset of SL(n,ℂ) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on the space of admissible elements in AN. We also show that the space of admissible elements is a multiplicative subset of AN. We establish a geometric...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/135167 |
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| _version_ | 1832564202844192768 |
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| author | Philip Foth |
| author_facet | Philip Foth |
| author_sort | Philip Foth |
| collection | DOAJ |
| description | We study the Iwasawa-type decomposition of an open subset of SL(n,ℂ) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on the
space of admissible elements in AN. We also show that the space of admissible elements
is a multiplicative subset of AN. We establish a geometric criterion: the symmetrization
of an admissible element maps the positive cone in ℂn into itself. |
| format | Article |
| id | doaj-art-72136cec62124359a16f1837ce4401c6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-72136cec62124359a16f1837ce4401c62025-02-03T01:11:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/135167135167A Note on Iwasawa-Type DecompositionPhilip Foth0CEGEP, Champlain St. Lawrence, QC, G1V 4K2, CanadaWe study the Iwasawa-type decomposition of an open subset of SL(n,ℂ) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on the space of admissible elements in AN. We also show that the space of admissible elements is a multiplicative subset of AN. We establish a geometric criterion: the symmetrization of an admissible element maps the positive cone in ℂn into itself.http://dx.doi.org/10.1155/2011/135167 |
| spellingShingle | Philip Foth A Note on Iwasawa-Type Decomposition International Journal of Mathematics and Mathematical Sciences |
| title | A Note on Iwasawa-Type Decomposition |
| title_full | A Note on Iwasawa-Type Decomposition |
| title_fullStr | A Note on Iwasawa-Type Decomposition |
| title_full_unstemmed | A Note on Iwasawa-Type Decomposition |
| title_short | A Note on Iwasawa-Type Decomposition |
| title_sort | note on iwasawa type decomposition |
| url | http://dx.doi.org/10.1155/2011/135167 |
| work_keys_str_mv | AT philipfoth anoteoniwasawatypedecomposition AT philipfoth noteoniwasawatypedecomposition |