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| Author(s): |
Matheus Batagini Brito
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2015-02-20 |
| Examining board members: |
Adriano Adrega de Moura;
Matthew Lyle Bennett;
Marines Guerreiro;
Bárbara Seelig Pogorelsky;
Renato Alessandro Martins
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| Advisor: | Adriano Adrega de Moura; Evgeny Mukhin |
| Abstract | |
We study finite--dimensional representations for a quantum affine algebra from two different points of view. In the first part of this work we study the graded limit of a certain subclass of irreducible representations. Let V be a finite--dimensional representation for a quantum affine algebra of type A and assume that V is isomorphic to the tensor product of a minimal affinization by parts whose highest weight is a sum of distinct fundamental weights by Kirillov-Reshetkhin modules whose highest weights are twice a fundamental weight. We prove that V admits a graded limit L and that L is isomorphic to a level-two Demazure module as well as to the fusion product of the graded limits of each of the aforementioned tensor factors of V. We also prove that if the quantum affine algebra is of classical type (resp. type G), the graded limit of (regular) minimal affinizations (resp. Kirillov--Reshetkin modules) are isomorphic to CV-modules for some R^+ partition explicitly described. In the second part we show that a module for the quantum affine algebra of type B and rank n is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized eigenspaces have dimension one. We classify all such modules and describe their q-characters. In some cases, the q-characters are described by super standard Young tableaux of type (2n|1) (AU) | |
| FAPESP's process: | 10/19458-9 - Classification and Structure of certain Representations of Quantum Affine Algebras |
| Grantee: | Matheus Batagini Brito |
| Support Opportunities: | Scholarships in Brazil - Doctorate |