Algorithms for Computations in Local Symmetric Spaces

Abstract

In this thesis, we use finite semisimple Lie theory to compute the structure of a local symmetric space p and its corresponding symmetric space P. Helminck classifies the local symmetric spaces over algebraically closed fields in [Hel88]. Here I extend these first results and write algorithms that implement combinatorial methods to compute `"nice" bases, restricted root systems, multiplicities and restricted Weyl groups for these spaces.

Description

Keywords

Lie Groups, Lie Algebras, Local Symmetric Spaces, Symmetric Spaces

Citation

Degree

PhD

Discipline

Mathematics

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