Iterative character constructions for algebra groups

作者：Marberg Eric^*

来源：Advances in Mathematics, 2011, 228(5): 2743-2765.

DOI：10.1016/j.aim.2011.05.029

• Supercharacters
• Kirillov functions
• Algebra group
• Pattern group
• Unitriangular group

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 x 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 sonic results related to counting the irreducible constituents of supercharacters.

• 出版日期2011-12-1