Counting irreducible representations of large degree of the upper triangular groups. (English) Zbl 1236.20049
Summary: Let \(U_n(q)\) be the upper triangular group of degree \(n\) over the finite field \(\mathbb F_q\) with \(q\) elements. In this paper, we present constructions of large degree (complex) irreducible representations of \(U_n(q)\) where \(n\geqslant 7\), and then determine the number of irreducible representations of largest, second largest and third largest degrees.
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 20G40 | Linear algebraic groups over finite fields |
Keywords:
tensor products; root systems; irreducible characters; irreducible complex representations; numbers of irreducible representations; triangular groups over finite fielddsReferences:
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