On a Parabolic Symmetry of Finite Coxeter Groups |
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| Authors: | Hohlweg Christophe; Schocker Manfred |
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| Institution: | Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS 7 rue René Descartes, 67084 Strasbourg Cedex, France hohlweg{at}math.u-strasbg.fr
Mathematical Institute 24–29 St. Giles', Oxford OX1 3LB, United Kingdom schocker{at}maths.ox.ac.uk |
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| Abstract: | Let (W, S be a finite Coxeter system, and let J S. Any w W hasa unique factorization w = wJ wJ, where wj belongs to the parabolicsubgroup WJ generated by J, and wJ is of minimal length in thecoset wWJ. It is shown here that wI = wJ if and only if wI =wJ, for all I, J S. Furthermore, a similar symmetry propertyin arbitrary (WI, WJ-double cosets is conjectured, which linksthis result to the Solomon descent algebra of W. 2000 MathematicsSubject Classification 20F55. |
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