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...

Full description

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/
id UNIANDES2_45b1ee828dbcaf8abe2f8507ababaa78
oai_identifier_str oai:repositorio.uniandes.edu.co:1992/51302
network_acronym_str UNIANDES2
network_name_str Séneca: repositorio Uniandes
repository_id_str
spelling 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
dc.type.redcol.spa.fl_str_mv 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/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv 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
institution Universidad de los Andes
bitstream.url.fl_str_mv https://repositorio.uniandes.edu.co/bitstreams/687f78e1-eaea-4bd0-ba8e-d28d59530c85/download
https://repositorio.uniandes.edu.co/bitstreams/6e13bef5-0c2a-459d-8b7c-3351911ce067/download
https://repositorio.uniandes.edu.co/bitstreams/2c78224f-d2a7-44af-9ffd-bb43021f0a82/download
bitstream.checksum.fl_str_mv 0ed7bc1534ba0173f9f46648fecb8ed5
9b42ac4aa013fa402a3e6325f82e055d
37521b707cec6f2068551f866017bf63
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
repository.name.fl_str_mv Repositorio institucional Séneca
repository.mail.fl_str_mv adminrepositorio@uniandes.edu.co
_version_ 1812133871950495744