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Unitary reflection groups and cohomology. (English) Zbl 0452.20050

MSC:
20H15 Other geometric groups, including crystallographic groups
20G10 Cohomology theory for linear algebraic groups
51F15 Reflection groups, reflection geometries
51F25 Orthogonal and unitary groups in metric geometry
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[1] Benard, M.: Characters and Schur indices of the unitary reflection group [321]3. Pacific J. Math.58, 309-321 (1975) · Zbl 0312.20005
[2] Benard, M.: Schur indices and splitting fields of the unitary reflection groups. J. Algebra38, 318-342 (1976) · Zbl 0327.20004 · doi:10.1016/0021-8693(76)90223-4
[3] Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4, 5 et 6. Paris: Hermann 1968 · Zbl 0186.33001
[4] Brieskorn, E.: Sur les groupes de tresses (d’après V.I. Arnol’d), Séminaire Bourbaki 24e année, 1971/2, Springer Lecture Notes No. 317, Berlin: Springer Verlag 1973
[5] Chevalley, C.: Invariants of finite groups generated by relfections. Amer. J. Math.77, 778-782 (1955) · Zbl 0065.26103 · doi:10.2307/2372597
[6] Coleman, A.J.: The Betti numbers of the simple Lie groups, Canadian J. Math.10, 349-356 (1958) · Zbl 0166.29702 · doi:10.4153/CJM-1958-034-2
[7] Coxeter, H.S.M.: The product of the generators of a finite group generated by reflections. Duke Math. J.18, 765-782 (1951) · Zbl 0044.25603 · doi:10.1215/S0012-7094-51-01870-4
[8] Coxeter, H.S.M.: Regular Complex Polytopes. Cambridge: Cambridge Univ. Press, 1974 · Zbl 0296.50009
[9] Flatto, L.: Invariants of finite reflection groups. L’Enseignement math.24, 237-292 (1978) · Zbl 0401.20041
[10] Gutkin, E.A.: Matrices connected with groups generated by mappings. Funct. Anal. and Appl. 7, 153-154 (1973) = Funkt. Anal. i Prilozen.7, 81-82 (1973) · Zbl 0324.20056 · doi:10.1007/BF01078889
[11] Koster, D.W.: Complex Reflection Groups. Thesis, Madison: University of Wisconsin 1975
[12] Orlik, P., Solomon, L.: Combinatorics and topology of complements of hyperplanes. Invent. math.56, 167-189 (1980) · Zbl 0432.14016 · doi:10.1007/BF01392549
[13] Parthasarathy, K.R., Ranga Rao, R., Varadarajan, V.S.: Representations of complex semi-simple Lie groups and Lie algebras. Annals of Math.85, 383-429 (1967) · Zbl 0177.18004 · doi:10.2307/1970351
[14] Shephard, G.C., Todd, J.A.: Finite unitary relfection groups. Canadian J. Math.6, 274-304 (1954) · Zbl 0055.14305 · doi:10.4153/CJM-1954-028-3
[15] Solomon, L.: Invariants of finite reflection groups. Nagoya Math. J.22, 57-64 (1963) · Zbl 0117.27104
[16] Solomon, L.: Invariants of Euclidean reflection groups. Trans. Amer. Math. Soc.113, 274-286 (1964) · Zbl 0142.26302 · doi:10.1090/S0002-9947-1964-0165038-3
[17] Springer, T.A.: Regular elements of finite reflection groups. Invent. math.25, 159-198 (1974) · Zbl 0287.20043 · doi:10.1007/BF01390173
[18] Stanley, R.P.: Relative invariants of finite groups generated by pseudoreflections. J. Algebra49, 134-148 (1977) · Zbl 0383.20029 · doi:10.1016/0021-8693(77)90273-3
[19] Steinberg, R.: Finite reflection groups. Trans. Amer. Math. Soc.91, 493-504 (1959) · Zbl 0092.13904 · doi:10.1090/S0002-9947-1959-0106428-2
[20] Steinberg, R.: Differential equations invariant under finite reflection groups. Trans. Amer. Math. Soc.112, 392-400 (1964) · Zbl 0196.39202 · doi:10.1090/S0002-9947-1964-0167535-3
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