---
source_url: "https://scite.ai/reports/10.1112/S0024611597000105"
title: ‘Good’ Elements of Finite Coxeter Groups and Representations of Iwahori-Hecke Algebras
mirrored_at: 2026-08-13T01:03:43.434Z
host: scite.ai
cited_in_42a: true
mirror_canonical: "https://index.42a.ai/scite.ai/reports/10.1112/S0024611597000105"
---

> **Original source:** https://scite.ai/reports/10.1112/S0024611597000105

“…It also follows from Proposition 6 that for any commutation class \[w\], distinct from \[w 0 \], there is a path from \[w\] to a class with a smaller S-value, which means that there is a path joining \[w\] and \[w 0 \]. Thus, we recover the following result from S. Elnitsky \[7\], which is also a consequence of Matsumoto's Theorem \[8\]. This result also follows from the fact that G(w) is connected for any w ∈ S n+1 \[9\].…”

**Section**: Radius Diameter and Planarity

supporting

confidence: 78%

“…Now suppose C is cuspidal. Then as remarked on p. 77 of \[GP00\], the fix-set of w in V , and thus in V \* , is trivial, so (2) holds. Therefore as Fix(w) and Mov(w) are orthogonal complements in V \* , we obtain (3).…”

**Section**: Cuspidal and Coxeter Elements

mentioning

confidence: 74%

“…It also follows from Proposition 6 that for any commutation class \[w\], distinct from \[w 0 \], there is a path from \[w\] to a class with a smaller S-value, which means that there is a path joining \[w\] and \[w 0 \]. Thus, we recover the following result from S. Elnitsky \[7\], which is also a consequence of Matsumoto's Theorem \[8\]. This result also follows from the fact that G(w) is connected for any w ∈ S n+1 \[9\].…”

**Section**: Radius Diameter and Planarity

supporting

confidence: 78%

“…The formulas for U 1 , U 2 and U 3 are easily deduced from that rule and the description of the principal Φ 2n -block given in Section 2.1. By \[22,Proposition 6.1.4\] we have R G M 1 2n = i 1 i .1 2n−i from which we deduce the value of U 4 from Section 2.1. □…”

**Section**: Annales De L'institut Fourier

mentioning

confidence: 72%

“…Now suppose C is cuspidal. Then as remarked on p. 77 of \[GP00\], the fix-set of w in V , and thus in V \* , is trivial, so (2) holds. Therefore as Fix(w) and Mov(w) are orthogonal complements in V \* , we obtain (3).…”

**Section**: Cuspidal and Coxeter Elements

mentioning

confidence: 74%