## DANIELE BRILLI

PhD Graduate**PhD program:**: XXXIII

**supervisor**: A. De Sole

**advisor**: A. D'Andrea

**Thesis title:**Pseudoalgebraic structures and representations of the exceptional Lie superalgebra E(5,10)

The language of Lie pseudoalgebras is useful in giving finite description of infinite-dimensional Lie algebras and has proved to be a valuable tool in algebra and representation theory. In this thesis, we apply pseudoalgebraic techniques to the representation theory of the exceptional linearly compact Lie superalgebra E(5,10). We construct a Lie super pseudoalgebra associated to E(5,10) and use it to find a bound on the degree of singular vectors in generalized Verma modules. We also classify all such pseudoalgebraic structures for E(5,10). We expect that the techniques developed can be suitably generalized.