Full text
| |
| Author(s): |
Maico Gouvêia de Oliveira Freitas
Total Authors: 1
|
| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2022-03-04 |
| Examining board members: |
Adriano Adrega de Moura;
Plamen Emilov Kochloukov;
Angelo Calil Biânchi
|
| Advisor: | Adriano Adrega de Moura |
| Abstract | |
Let g be the Lie algebra of traceless (n+1)×(n+1) matrices. The Schur-Weyl duality is a classical result that establishes an equivalence of categories between the category of finite-dimensional modules for the symmetric group and a certain category of representations of g. In Chari and Pressley's article Quantum Affine Algebras and Affine Hecke Algebras, a version of this result was established with the role of the symmetric group being played by the affine Hecke algebra and the role of g being played by the quantum affine algebra over g. In particular, the authors claimed that an analogous proof scheme should provide another version of the Schur-Weyl duality, here referred to as the affine Schur-Weyl duality, in which the role of the symmetric group is played by the extended affine symmetric group and the role of g is played by the affine Lie algebra over g. Carrying out this scheme thoroughly, thus obtaining in the setting of the modules related by the affine Shcur-Weyl duality all the results analogous to those in Chari and Pressley's article, is the main objective of the present work. Going beyond the results of this article, we also set an investigation in the direction of describing the modules corresponding, via the affine Schur-Weyl duality, to the so-called local Weyl modules, which are relevant objects in the setting of finite-dimensional representations of the affine Lie algebra over g that were not yet introduced in the literature by the time that Chari and Pressley's article was published (AU) | |
| FAPESP's process: | 19/23380-0 - Weyl modules and Frobenius-Schur duality |
| Grantee: | Maico Gouveia de Oliveira Freitas |
| Support Opportunities: | Scholarships in Brazil - Master |