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| Author(s): |
Lucas Henrique Calixto
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: | 2015-04-12 |
| Examining board members: |
Adriano Adrega de Moura;
Kostiantyn Iusenko;
Viktor Bekkert;
Lucio Centrone;
Plamen Emilov Kochloukov
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| Advisor: | Adriano Adrega de Moura; Alistair Rowland John Savage |
| Abstract | |
This thesis is concerned with the representation theory of map Lie superalgebras. We consider a Lie superalgebra of the form $\g\otimes A$, where $A$ is an associative commutative unital $\C$-algebra and $\g$ is Lie superalgebra. Given actions of a finite group $\Gamma$ on both $A$ and $\g$, by automorphisms, we also consider the subalgebra of $\g\otimes A$ of points fixed by the associated action of $\Gamma$, which will be called an equivariant map superalgebra. In the first part of the thesis we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras (i.e. when the Lie superalgebra $\g$ is $\q(n)$, $n\geq 2$) under the assumption that $\Gamma$ is abelian and acts freely on $\MaxSpec (A)$. We show that the isomorphism classes of such representations are parametrized by a set of $\Gamma$-equivariant finitely supported maps from $\MaxSpec (A)$ to the set of isomorphism classes of irreducible finite-dimensional representations of $\g$. In the special case that $A$ is the coordinate ring of the torus, we obtain a classification of all irreducible finite-dimensional representations of the twisted loop queer superalgebra. In the second part of the thesis, we define global and local Weyl modules for $\g \otimes A$ with $\g$ a basic Lie superalgebra or $\fsl(n,n)$, $n \ge 2$. Under some mild assumptions, we prove universality, finite-dimensionality, and tensor product decomposition properties for these modules. We define super-Weyl functors for these Lie superalgebras and we prove several properties that are analogues of those of Weyl functors in the non-super setting. We also point out some features that are new in the super case (AU) | |
| FAPESP's process: | 13/08430-4 - Representations of map superalgebras |
| Grantee: | Lucas Henrique Calixto |
| Support Opportunities: | Scholarships in Brazil - Doctorate |