[{"issue":"1","publication_status":"published","publication_identifier":{"issn":["0305-0041","1469-8064"]},"citation":{"chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i> 175, no. 1 (2023): 129–60. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>.","ieee":"A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, pp. 129–160, 2023, doi: <a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","ama":"Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2023;175(1):129-160. doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>","short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160.","mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","bibtex":"@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160} }","apa":"Ernst, A., &#38; Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>175</i>(1), 129–160. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>"},"page":"129-160","intvolume":"       175","year":"2023","author":[{"first_name":"Alena","id":"46953","full_name":"Ernst, Alena","last_name":"Ernst"},{"first_name":"Kai-Uwe","full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt"}],"date_created":"2024-04-17T12:23:18Z","volume":175,"publisher":"Cambridge University Press (CUP)","date_updated":"2024-05-07T08:29:59Z","doi":"10.1017/s0305004123000075","title":"Intersection theorems for finite general linear groups","type":"journal_article","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","status":"public","user_id":"46953","department":[{"_id":"100"}],"_id":"53533","language":[{"iso":"eng"}],"keyword":["General Mathematics"]},{"title":"Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group","doi":"10.1017/s0305004100071577","date_updated":"2022-01-06T06:52:53Z","author":[{"last_name":"Melbourne","full_name":"Melbourne, Ian","first_name":"Ian"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"date_created":"2020-04-16T08:31:40Z","year":"1993","page":"235-268","citation":{"chicago":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 1993, 235–68. <a href=\"https://doi.org/10.1017/s0305004100071577\">https://doi.org/10.1017/s0305004100071577</a>.","ieee":"I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, pp. 235–268, 1993.","ama":"Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 1993:235-268. doi:<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>","apa":"Melbourne, I., &#38; Dellnitz, M. (1993). Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 235–268. <a href=\"https://doi.org/10.1017/s0305004100071577\">https://doi.org/10.1017/s0305004100071577</a>","mla":"Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian Vector Fields Commuting with the Action of a Compact Lie Group.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, 1993, pp. 235–68, doi:<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>.","short":"I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical Society (1993) 235–268.","bibtex":"@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}, DOI={<a href=\"https://doi.org/10.1017/s0305004100071577\">10.1017/s0305004100071577</a>}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Melbourne, Ian and Dellnitz, Michael}, year={1993}, pages={235–268} }"},"publication_identifier":{"issn":["0305-0041","1469-8064"]},"publication_status":"published","language":[{"iso":"eng"}],"_id":"16633","department":[{"_id":"101"}],"user_id":"15701","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.</jats:p><jats:p>Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.</jats:p>","lang":"eng"}],"status":"public","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","type":"journal_article"}]