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Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function. (English) Zbl 0333.20041

MSC:
20H15 Other geometric groups, including crystallographic groups
06F15 Ordered groups
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References:
[1] Bernstein, I. N., Gelfand, I. M., Gelfand, S. I.: Differential operators on the base affine space and a study ofg-modules, Lie groups and their representation. Summer School of Bolyai János Math. Soc., I. M. Gelfand, ed., pp. 21?64. New York: Halsted Press 1975 · Zbl 0338.58019
[2] Borel, A., Tits, J.: Compléments a l’article ?Groupes Reductifs?. Publ. Math. I.H.E.S.41, 253?276 (1972) · Zbl 0254.14018
[3] Bourbaki, N.: Groupes et Algebres de Lie. Chapitre 4, 5 et 6. Paris: Hermann 1968 · Zbl 0186.33001
[4] Rota, G. C.: On the foundations of combinatorial theory; I. Theory of Mobius functions. Z. Wahrscheinlichkeitstheorie verw. Gebiete Vol.2, 340?368 (1964) · Zbl 0121.02406
[5] Steinberg, R.: Lecture notes on Chevalley groups, mimeographed notes. Yale University, 1967
[6] Verma, D.-N.: Möbius inversion for the Bruhat ordering on a Weyl group. Ann. scient. Éc. Norm. Sup., 393?399 (1971) · Zbl 0236.20035
[7] Verma, D.-N.: A strengthening of the exchange condition property for Coxeter groups. Preprint 1972
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