Abstract
We give a classification of irreducible representations of generalized Heisenberg groups which is the pattern group associated to the closed set {(1, i), (2, j), (s, n − 1), (t, n) | 2 ≤ i ≤ n, 3 ≤ j ≤ n, 3 ≤ s < n − 1, 3 ≤ t < n}. In light of the conjectures of Higman, Lehrer and Isaacs for unitriangular groups, this result shows that the number of irreducible characters of
with a fixed degree is a polynomial in q−1 with non-negative integer coefficients.
Acknowledgments
The author is very grateful to the reviewer for his careful reading and suggestions for improving the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).