The maximal tori theorem and the mackey machinery
The objective of this project is to document two of the results used in the study of representations of compact Lie groups, these are: The Maximal Tori Theoremand Mackey's Normal Subgroup Analysis or machinery. The first of these results establishes that given a compact Lie group G, every eleme...
- Autores:
-
Zárate Guevara, John Sebastián
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2020
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/51302
- Acceso en línea:
- http://hdl.handle.net/1992/51302
- Palabra clave:
- Grupos de Lie
Grupos algebraicos
Matemáticas
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Angel Cárdenas, Jairo Andrésf778c8c5-d503-4a6f-81cc-a8efddc2f310500Zárate Guevara, John Sebastián9e2cedac-b459-423c-a8b6-08674bd1ac31500Galindo Martínez, César Neyit2021-08-10T18:19:26Z2021-08-10T18:19:26Z2020http://hdl.handle.net/1992/5130223614.pdfinstname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/The objective of this project is to document two of the results used in the study of representations of compact Lie groups, these are: The Maximal Tori Theoremand Mackey's Normal Subgroup Analysis or machinery. The first of these results establishes that given a compact Lie group G, every element of G is contained in a maximal torus and that the maximal tori are conjugated to each other. Given T a maximal torus with normalizer N, the quotient group W = N / T is known asthe Weyl group. A consequence of the maximal tori theorem is that the invariantfunctions under conjugation of G are in correspondence with the torus functions invariant under the action of W. This allows us to understand the characters of the representations of G, and, consequently, gives us information about the representations themselves. On the other hand, the second result gives us a way to calculate explicitly the decomposition...El objetivo de este proyecto es documentar dos de los resultados utilizados en el estudio de representaciones de grupos de Lie compactos, estos son: el teorema de los toros maximales y el análisis de subgrupos normales de Mackey o maquinaria de Mackey. El primero de estos resultados establece que dado un grupo de Lie compacto G, cada elemento de G está contenido en un toro maximal y que los toros maximales son conjugados entre sí. Dado T un toro maximal con normalizador N, el grupo cociente W = N / T se conoce como grupo Weyl. Una consecuencia del teorema de los toros maximales es que las funciones invariantes bajo conjugación de G están en correspondencia con las funciones del toro invariantes bajo la acción de W. Esto nos permite comprender los caracteres de las representaciones de G y, en consecuencia, nos da información sobre las representaciones de G. Por otro lado...MatemáticoPregrado42 hojasapplication/pdfengUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de MatemáticasThe maximal tori theorem and the mackey machineryTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesishttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/TPGrupos de LieGrupos algebraicosMatemáticasMatemáticas201530579PublicationORIGINAL23614.pdfapplication/pdf337385https://repositorio.uniandes.edu.co/bitstreams/687f78e1-eaea-4bd0-ba8e-d28d59530c85/download0ed7bc1534ba0173f9f46648fecb8ed5MD51TEXT23614.pdf.txt23614.pdf.txtExtracted texttext/plain59746https://repositorio.uniandes.edu.co/bitstreams/6e13bef5-0c2a-459d-8b7c-3351911ce067/download9b42ac4aa013fa402a3e6325f82e055dMD54THUMBNAIL23614.pdf.jpg23614.pdf.jpgIM Thumbnailimage/jpeg7374https://repositorio.uniandes.edu.co/bitstreams/2c78224f-d2a7-44af-9ffd-bb43021f0a82/download37521b707cec6f2068551f866017bf63MD551992/51302oai:repositorio.uniandes.edu.co:1992/513022023-10-10 16:19:23.463http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co |
dc.title.spa.fl_str_mv |
The maximal tori theorem and the mackey machinery |
title |
The maximal tori theorem and the mackey machinery |
spellingShingle |
The maximal tori theorem and the mackey machinery Grupos de Lie Grupos algebraicos Matemáticas Matemáticas |
title_short |
The maximal tori theorem and the mackey machinery |
title_full |
The maximal tori theorem and the mackey machinery |
title_fullStr |
The maximal tori theorem and the mackey machinery |
title_full_unstemmed |
The maximal tori theorem and the mackey machinery |
title_sort |
The maximal tori theorem and the mackey machinery |
dc.creator.fl_str_mv |
Zárate Guevara, John Sebastián |
dc.contributor.advisor.none.fl_str_mv |
Angel Cárdenas, Jairo Andrés |
dc.contributor.author.none.fl_str_mv |
Zárate Guevara, John Sebastián |
dc.contributor.jury.none.fl_str_mv |
Galindo Martínez, César Neyit |
dc.subject.armarc.none.fl_str_mv |
Grupos de Lie Grupos algebraicos Matemáticas |
topic |
Grupos de Lie Grupos algebraicos Matemáticas Matemáticas |
dc.subject.themes.none.fl_str_mv |
Matemáticas |
description |
The objective of this project is to document two of the results used in the study of representations of compact Lie groups, these are: The Maximal Tori Theoremand Mackey's Normal Subgroup Analysis or machinery. The first of these results establishes that given a compact Lie group G, every element of G is contained in a maximal torus and that the maximal tori are conjugated to each other. Given T a maximal torus with normalizer N, the quotient group W = N / T is known asthe Weyl group. A consequence of the maximal tori theorem is that the invariantfunctions under conjugation of G are in correspondence with the torus functions invariant under the action of W. This allows us to understand the characters of the representations of G, and, consequently, gives us information about the representations themselves. On the other hand, the second result gives us a way to calculate explicitly the decomposition... |
publishDate |
2020 |
dc.date.issued.none.fl_str_mv |
2020 |
dc.date.accessioned.none.fl_str_mv |
2021-08-10T18:19:26Z |
dc.date.available.none.fl_str_mv |
2021-08-10T18:19:26Z |
dc.type.spa.fl_str_mv |
Trabajo de grado - Pregrado |
dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/bachelorThesis |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_7a1f |
dc.type.content.spa.fl_str_mv |
Text |
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http://purl.org/redcol/resource_type/TP |
format |
http://purl.org/coar/resource_type/c_7a1f |
dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/1992/51302 |
dc.identifier.pdf.none.fl_str_mv |
23614.pdf |
dc.identifier.instname.spa.fl_str_mv |
instname:Universidad de los Andes |
dc.identifier.reponame.spa.fl_str_mv |
reponame:Repositorio Institucional Séneca |
dc.identifier.repourl.spa.fl_str_mv |
repourl:https://repositorio.uniandes.edu.co/ |
url |
http://hdl.handle.net/1992/51302 |
identifier_str_mv |
23614.pdf instname:Universidad de los Andes reponame:Repositorio Institucional Séneca repourl:https://repositorio.uniandes.edu.co/ |
dc.language.iso.none.fl_str_mv |
eng |
language |
eng |
dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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info:eu-repo/semantics/openAccess |
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http://purl.org/coar/access_right/c_abf2 |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ http://purl.org/coar/access_right/c_abf2 |
eu_rights_str_mv |
openAccess |
dc.format.extent.none.fl_str_mv |
42 hojas |
dc.format.mimetype.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidad de los Andes |
dc.publisher.program.none.fl_str_mv |
Matemáticas |
dc.publisher.faculty.none.fl_str_mv |
Facultad de Ciencias |
dc.publisher.department.none.fl_str_mv |
Departamento de Matemáticas |
publisher.none.fl_str_mv |
Universidad de los Andes |
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Universidad de los Andes |
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