Exotic characters of unitriangular matrix groups
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- 作者：Eric Marberga ; ; emarberg@math.mit.edu
- 刊名：Journal of Pure and Applied Algebra
- 出版年：2012
- 出版时间：February 2012
- 年：2012
- 卷：216
- 期：2
- 页码：239-254
- 全文大小：351 K
文摘
Let denote the unitriangular group of unipotent upper triangular matrices over a finite field with cardinality and prime characteristic . It has been known for some time that when is fixed and is sufficiently large, has ¡°exotic?irreducible characters taking values outside the cyclotomic field . However, all proofs of this fact to date have been both non-constructive and computer dependent. In the preliminary work Marberg (2010) , we defined a family of orthogonal characters decomposing the supercharacters of an arbitrary algebra group. By applying this construction to the unitriangular group, we are able to derive by hand an explicit description of a family of characters of taking values in arbitrarily large cyclotomic fields. In particular, we prove that if is a positive integer power of and , then has an irreducible character of degree which takes values outside . By the same techniques, we are also able to construct explicit Kirillov functions which fail to be characters of when and is arbitrary.