On the construction of a finite Siegel space
- Autores
- Pantoja, Jose; Soto Andrade, Jorge; Vargas, Jorge Antonio
- Año de publicación
- 2015
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We construct a finite analogue of classical Siegel’s Space. This is made by generalizing Poincar´e half plane construction for a quadratic field extension E ⊃ F, considering in this case an involutive ring A, extension of the ring fixed points A0 = AΓ, (Γ an order two group of automorphisms of A), and the generalized special linear group SL∗(2, A), which acts on a certain ∗− plane PA. Classical Lagrangians for finite dimensional spaces over a finite field are related with Lagrangians for PA. We show SL∗(2, A) acts transitively on PA when A is a ∗− euclidean ring, and we study extensibly the case where A = Mn(E). The structure of the orbits of the action of the symplectic group over F on Lagrangians over a finite dimensional space over E are studied.
Fil: Pantoja, Jose. Pontificia Universidad Católica de Chile; Chile
Fil: Soto Andrade, Jorge. Universidad de Chile; Chile
Fil: Vargas, Jorge Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina - Materia
-
Finite Siegel Upper Half Space
Star-Analogue - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/51914
Ver los metadatos del registro completo
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On the construction of a finite Siegel spacePantoja, JoseSoto Andrade, JorgeVargas, Jorge AntonioFinite Siegel Upper Half SpaceStar-Analoguehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We construct a finite analogue of classical Siegel’s Space. This is made by generalizing Poincar´e half plane construction for a quadratic field extension E ⊃ F, considering in this case an involutive ring A, extension of the ring fixed points A0 = AΓ, (Γ an order two group of automorphisms of A), and the generalized special linear group SL∗(2, A), which acts on a certain ∗− plane PA. Classical Lagrangians for finite dimensional spaces over a finite field are related with Lagrangians for PA. We show SL∗(2, A) acts transitively on PA when A is a ∗− euclidean ring, and we study extensibly the case where A = Mn(E). The structure of the orbits of the action of the symplectic group over F on Lagrangians over a finite dimensional space over E are studied.Fil: Pantoja, Jose. Pontificia Universidad Católica de Chile; ChileFil: Soto Andrade, Jorge. Universidad de Chile; ChileFil: Vargas, Jorge Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaHeldermann Verlag2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/51914Pantoja, Jose; Soto Andrade, Jorge; Vargas, Jorge Antonio; On the construction of a finite Siegel space; Heldermann Verlag; Journal Of Lie Theory; 25; 11-2015; 1045-10710949-5932CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT25/JLT254/jlt25048.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:05:30Zoai:ri.conicet.gov.ar:11336/51914instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:05:31.099CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On the construction of a finite Siegel space |
| title |
On the construction of a finite Siegel space |
| spellingShingle |
On the construction of a finite Siegel space Pantoja, Jose Finite Siegel Upper Half Space Star-Analogue |
| title_short |
On the construction of a finite Siegel space |
| title_full |
On the construction of a finite Siegel space |
| title_fullStr |
On the construction of a finite Siegel space |
| title_full_unstemmed |
On the construction of a finite Siegel space |
| title_sort |
On the construction of a finite Siegel space |
| dc.creator.none.fl_str_mv |
Pantoja, Jose Soto Andrade, Jorge Vargas, Jorge Antonio |
| author |
Pantoja, Jose |
| author_facet |
Pantoja, Jose Soto Andrade, Jorge Vargas, Jorge Antonio |
| author_role |
author |
| author2 |
Soto Andrade, Jorge Vargas, Jorge Antonio |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Finite Siegel Upper Half Space Star-Analogue |
| topic |
Finite Siegel Upper Half Space Star-Analogue |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
We construct a finite analogue of classical Siegel’s Space. This is made by generalizing Poincar´e half plane construction for a quadratic field extension E ⊃ F, considering in this case an involutive ring A, extension of the ring fixed points A0 = AΓ, (Γ an order two group of automorphisms of A), and the generalized special linear group SL∗(2, A), which acts on a certain ∗− plane PA. Classical Lagrangians for finite dimensional spaces over a finite field are related with Lagrangians for PA. We show SL∗(2, A) acts transitively on PA when A is a ∗− euclidean ring, and we study extensibly the case where A = Mn(E). The structure of the orbits of the action of the symplectic group over F on Lagrangians over a finite dimensional space over E are studied. Fil: Pantoja, Jose. Pontificia Universidad Católica de Chile; Chile Fil: Soto Andrade, Jorge. Universidad de Chile; Chile Fil: Vargas, Jorge Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina |
| description |
We construct a finite analogue of classical Siegel’s Space. This is made by generalizing Poincar´e half plane construction for a quadratic field extension E ⊃ F, considering in this case an involutive ring A, extension of the ring fixed points A0 = AΓ, (Γ an order two group of automorphisms of A), and the generalized special linear group SL∗(2, A), which acts on a certain ∗− plane PA. Classical Lagrangians for finite dimensional spaces over a finite field are related with Lagrangians for PA. We show SL∗(2, A) acts transitively on PA when A is a ∗− euclidean ring, and we study extensibly the case where A = Mn(E). The structure of the orbits of the action of the symplectic group over F on Lagrangians over a finite dimensional space over E are studied. |
| publishDate |
2015 |
| dc.date.none.fl_str_mv |
2015-11 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/51914 Pantoja, Jose; Soto Andrade, Jorge; Vargas, Jorge Antonio; On the construction of a finite Siegel space; Heldermann Verlag; Journal Of Lie Theory; 25; 11-2015; 1045-1071 0949-5932 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/51914 |
| identifier_str_mv |
Pantoja, Jose; Soto Andrade, Jorge; Vargas, Jorge Antonio; On the construction of a finite Siegel space; Heldermann Verlag; Journal Of Lie Theory; 25; 11-2015; 1045-1071 0949-5932 CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
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eng |
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info:eu-repo/semantics/altIdentifier/url/http://www.heldermann.de/JLT/JLT25/JLT254/jlt25048.htm |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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Heldermann Verlag |
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