A. Miller

collaborators

3 papers

math.RT2025

Denseness results for zeros and roots of unity in character tables

Alexander R. Miller

For any irreducible character $I ¨ $ of a finite group $G$ , let $I^¸ (I ¨ )$ denote the proportion of elements $g \in G$ for which $I ¨ (g)$ is either zero or a root of unity. Then for any…

math.RT2025

Covering numbers for characters of symmetric groups

Alexander R. Miller

If $n > 4$ and $c (I^¸)$ denotes the set of irreducible constituents of a character $I^¸$ , then $c (I ¨ ^{k}) = Irr (S_{n})$ for all nonlinear $I ¨ \in Irr (S_{n})$ if and only if $k\geq n…

math.GR2024

Short character values on large conjugacy classes

Alexander R. Miller

We provide an example of a finite group with a conjugacy class of average size on which fewer than half of the irreducible characters are either zero or a root of unity.