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

• Anna E. Bargagliotti Department of Mathematics, Loyola Marymount University, Los Angeles, CA
• Michael Orrison Harvey Mudd College

Abstract

Let $$G$$ be a finite group, let $$\mathbb{C}G$$ be the complex group algebra of $$G$$, and let $$p \in \mathbb{C}G$$. In this paper, we show how to construct submodules$$S$$ of $$\mathbb{C}G$$ 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 $$S_n$$ 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.

Published
2018-09-24
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Section
Articles