Iterative character constructions for algebra groups |
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Authors: | Eric Marberg |
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Institution: | Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States |
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Abstract: | We construct a family of orthogonal characters of an algebra group which decompose the supercharacters defined by Diaconis and Isaacs (2008) 6]. Like supercharacters, these characters are given by nonnegative integer linear combinations of Kirillov functions and are induced from linear supercharacters of certain algebra subgroups. We derive a formula for these characters and give a condition for their irreducibility; generalizing a theorem of Otto (2010) 20], we also show that each such character has the same number of Kirillov functions and irreducible characters as constituents. In proving these results, we observe as an application how a recent computation by Evseev (2010) 7] implies that every irreducible character of the unitriangular group UTn(q) of unipotent n×n upper triangular matrices over a finite field with q elements is a Kirillov function if and only if n?12. As a further application, we discuss some more general conditions showing that Kirillov functions are characters, and describe some results related to counting the irreducible constituents of supercharacters. |
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Keywords: | Supercharacters Kirillov functions Algebra group Pattern group Unitriangular group |
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