An Eigenspace Approach to Decomposing Representations of Finite Groups
نویسندگان
چکیده
The first half of this thesis develops an eigenspace approach to computing the basisindependent isotypic decomposition of a vector in a representation of a finite group. The approach takes advantage of well-chosen diagonalizable linear transformations to compute isotypic projections through a series of eigenspace projections, and at its heart is an efficient eigenspace projection method built around a modified GramSchmidt algorithm known as the Lanczos iteration. In the second half, it is shown how this eigenspace approach gives rise to an efficient decomposition method for permutation representations of distance transitive graphs, the symmetric group, the hyperoctahedral group, the finite general linear group, and the finite symplectic group.
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