Variedades de caracteres y su relación con los fibrados principales de Higgs
DOI:
https://doi.org/10.15517/vv48fd28Palabras clave:
Variedades de caracteres, Retracción de deformación, Fibrados principales, Fibrados principales de Higgs, Branas, Representaciones de SchottkyResumen
En primer lugar, se revisan las nociones de grupos de Lie y grupos algebraicos, tanto reales como complejos, así como de grupos finitamente generados, que constituyen ingredientes esenciales en la definición de una variedad de caracteres. A continuación, se analiza el espacio de representaciones de un grupo finitamente generado en un grupo de Lie o en un grupo algebraico, atendiendo a su topología, su estructura de variedad, su espacio tangente y la acción por conjugación de este último grupo. Posteriormente, se construye el cociente respecto de esta acción, la variedad de caracteres, presentando distintos enfoques para dicha construcción. Asimismo, se estudia la existencia de retracciones por deformación entre variedades de caracteres al considerar subgrupos compactos máximos del grupo de Lie. Finalmente, se aborda la correspondencia entre representaciones de grupos de superficies y haces principales, con especial atención a las representaciones de Schottky, y se relacionan estas construcciones con el marco geométrico de los fibrados principales de Higgs y las branas. Esta perspectiva sugiere nuevas direcciones que conectan la teoría de representaciones, la correspondencia de Hodge no abeliana y la geometría de los espacios de módulos.
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Derechos de autor 2026 Ana Cristina Casimiro (Autor/a)
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