Some Geometry of Symmetrized Tensor Spaces
Type of Degreedissertation
Mathematics and Statistics
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In this paper we investigate the geometry of symmetrized tensor spaces using a construct known as a coset space. We find that, for a group G, certain pairings of subgroups and irreducible characters give rise to crystallographic root systems. We also gain insight into the conditions under which a symmetrized tensor space has an o-basis.