Maximal Length Projections in Group Algebras with Applications to Linear Rank Tests of Uniformity

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. Article