Algorithms for Computations in Local Symmetric Spaces

Please use this identifier to cite or link to this item: http://www.lib.ncsu.edu/resolver/1840.16/4525

Title:	Algorithms for Computations in Local Symmetric Spaces
Authors:	Fowler, Jennifer Renee
Advisors:	Jack W. Silverstein, Committee Member Aloysius G. Helminck, Committee Chair Amassa Fauntleroy, Committee Member Ernest L. Stitzinger, Committee Member
Keywords:	Lie Groups Lie Algebras Local Symmetric Spaces Symmetric Spaces
Issue Date:	17-Apr-2003
Degree:	PhD
Discipline:	Mathematics
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.
URI:	http://www.lib.ncsu.edu/resolver/1840.16/4525
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