An algorithm for calculating characters of Hecke algebras \(H_ n(q)\) of type \(A_{n-1}\) when \(q\) is a root of unity. (English) Zbl 0795.20024
Recently, a Frobenius character formula was found for the characters \(\varphi_ \rho^ \sigma(q)\) of the irreducible representations \(\pi_{[\sigma]}\) of the Hecke algebra \(H_ n(q)\) (of type \(A_{n-1}\)) labelled by \((m,k)\)-standard partitions \(\sigma\), where \(q\) is a primitive \(p\)th root of unity with \(p=m+k\) [see the preceding review, Zbl 0795.20023]. Here, this result is used to derive a combinatorial procedure for calculating these characters. This procedure generalizes that of Murnaghan and Nakayama for characters of \(S_ n\), and a more recent one for characters of \(H_ n(q)\) for generic \(q\).
Reviewer: J.Van der Jeugt (Gent)
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 05E10 | Combinatorial aspects of representation theory |
| 20C30 | Representations of finite symmetric groups |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Citations:
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