Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Length Function and Admissible Diagrams for Complex Reflection Groups G(m, 1, n)

  • Can, Himmet (Department of Mathematics, Faculty of Arts and Sciences, Erciyes University)
  • Received : 2004.02.11
  • Published : 2005.06.23
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Abstract

In this paper, we introduce a length function for elements of the imprimitive complex reflection group G(m, 1, n) and study its properties. Furthermore, we show that every conjugacy class of G(m, 1, n) can be represented by an admissible diagram. The corresponding results for Weyl groups are well known.

Keywords

References

  1. Contrib. Alg. Geom. v.37 no.2 Representations of the generalized symmetric groups Can, H.
  2. Comm. Algebra v.26 no.8 Representations of the imprimitive complex reflection groups G(m, 1, n) Can, H.
  3. European J. Combin. v.19 Some combinatorial results for complex reflection groups Can, H.
  4. Ars Combinatoria v.58 A computer program for obtaining subsystems Can, H.;Hawkins, L.
  5. Algebra Colloquium Subsystems of the complex root systems Can, H.
  6. Compositio Math. v.25 Conjugacy classes in the Weyl group Carter, R.W.
  7. Ann. Scient. Ec. Norm. Sup. v.4 no.9 Finite complex reflection groups Cohen, A.M.
  8. J. London Math. Soc. v.8 The Schur multiplier of the generalized symmetric group Davies, J.W.;Morris, A.O.
  9. Lecture Notes in Mathematics v.240 Representations of Permutation Groups I. Kerber, A.
  10. J. Algebra v.45 no.2 On the finite imprimitive unitary reflection groups Read, E.W.
  11. Am. Math. Soc. Transl. v.112 Differential equations invariant under finite reflection groups Steinberg, R.