Representations of nilpotent groups on spaces with indefinite metric
The paper studies the structure of J-unitary representations of connected nilpotent groups on Πk-spaces, that is, the representations on a Hilbert space preserving a quadratic form “with a finite number of negative squares”. Apart from some comparatively simple cases, such representations can be rea...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2016
|
| Subjects: | |
| Online Access: | https://repository.londonmet.ac.uk/1195/7/REPRESENTATIONS%20OF%20NILPOTENT%20ON%20SPACES%20WITH%20INDEFINITE%20METRIC.pdf |
| _version_ | 1804071643381760000 |
|---|---|
| author | Kissin, Edward Shulman, Victor S. |
| author_facet | Kissin, Edward Shulman, Victor S. |
| author_sort | Kissin, Edward |
| collection | LMU |
| description | The paper studies the structure of J-unitary representations of connected nilpotent groups on Πk-spaces, that is, the representations on a Hilbert space preserving a quadratic form “with a finite number of negative squares”. Apart from some comparatively simple cases, such representations can be realized as double extensions of finite-dimensional representations by unitary ones. So their study is based on some special cohomological technique. We concentrate mostly on the problems of the decomposition of these representations and the classification of “non-decomposable” ones. |
| first_indexed | 2024-07-09T03:46:31Z |
| format | Article |
| id | oai:repository.londonmet.ac.uk:1195 |
| institution | London Metropolitan University |
| language | English |
| last_indexed | 2024-07-09T03:46:31Z |
| publishDate | 2016 |
| publisher | Springer International Publishing |
| record_format | eprints |
| spelling | oai:repository.londonmet.ac.uk:11952020-05-29T16:06:34Z http://repository.londonmet.ac.uk/1195/ Representations of nilpotent groups on spaces with indefinite metric Kissin, Edward Shulman, Victor S. 510 Mathematics The paper studies the structure of J-unitary representations of connected nilpotent groups on Πk-spaces, that is, the representations on a Hilbert space preserving a quadratic form “with a finite number of negative squares”. Apart from some comparatively simple cases, such representations can be realized as double extensions of finite-dimensional representations by unitary ones. So their study is based on some special cohomological technique. We concentrate mostly on the problems of the decomposition of these representations and the classification of “non-decomposable” ones. Springer International Publishing 2016-12-31 Article PeerReviewed text en https://repository.londonmet.ac.uk/1195/7/REPRESENTATIONS%20OF%20NILPOTENT%20ON%20SPACES%20WITH%20INDEFINITE%20METRIC.pdf Kissin, Edward and Shulman, Victor S. (2016) Representations of nilpotent groups on spaces with indefinite metric. Journal of Integral Equations and Operator Theory. ISSN 0378-620X 10.1007/s00020-016-2337-7 |
| spellingShingle | 510 Mathematics Kissin, Edward Shulman, Victor S. Representations of nilpotent groups on spaces with indefinite metric |
| title | Representations of nilpotent groups on spaces with indefinite metric |
| title_full | Representations of nilpotent groups on spaces with indefinite metric |
| title_fullStr | Representations of nilpotent groups on spaces with indefinite metric |
| title_full_unstemmed | Representations of nilpotent groups on spaces with indefinite metric |
| title_short | Representations of nilpotent groups on spaces with indefinite metric |
| title_sort | representations of nilpotent groups on spaces with indefinite metric |
| topic | 510 Mathematics |
| url | https://repository.londonmet.ac.uk/1195/7/REPRESENTATIONS%20OF%20NILPOTENT%20ON%20SPACES%20WITH%20INDEFINITE%20METRIC.pdf |
| work_keys_str_mv | AT kissinedward representationsofnilpotentgroupsonspaceswithindefinitemetric AT shulmanvictors representationsofnilpotentgroupsonspaceswithindefinitemetric |