Maximal Length Projections in Group Algebras with Applications to Linear Rank Tests of Uniformity
Bargagliotti, Anna E.
Creator
Faculty
orrison@g.hmc.edu
Orrison, Michael
Creator
MATH / Applied Mathematics
Illinois Institute of Technology
Affiliated department
Group algebra
Plancherel formula
singular value decomposition
Wedderburn decomposition
linear rank tests of uniformity
Let G be a finite group, let CG be the complex group algebra of G, and let p ∈ CG. In this paper, we show how to construct submodules S of CG of a fixed dimension with the property that the orthogonal projection of p onto S has maximal length. We then provide an example of how such submodules for the symmetric group Sn can be used to create new linear rank tests of uniformity in statistics for survey data that arises when respondents are asked to give a complete ranking of n items.
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