Geodesic
STAR REDUCIBLE COXETER GROUPS
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 583-609

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DOI

We define “star reducible” Coxeter groups to be those Coxeter groups for which every fully commutative element (in the sense of Stembridge) is equivalent to a product of commuting generators by a sequence of length-decreasing star operations (in the sense of Lusztig). We show that the Kazhdan–Lusztig bases of these groups have a nice projection property to the Temperley–Lieb type quotient, and furthermore that the images of the basis elements $C'_w$ (for fully commutative $w$) in the quotient have structure constants in ${\mathbb Z}^{\geq 0}[v, v^{-1}]$. We also classify the star reducible Coxeter groups and show that they form nine infinite families with two exceptional cases.
DOI : 10.1017/S0017089506003211
Mots-clés : 20F55, 20C08 
GREEN, R. M. STAR REDUCIBLE COXETER GROUPS. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 583-609. doi: 10.1017/S0017089506003211
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     title = {STAR {REDUCIBLE} {COXETER} {GROUPS}},
     journal = {Glasgow mathematical journal},
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     year = {2006},
     volume = {48},
     number = {3},
     doi = {10.1017/S0017089506003211},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003211/}
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