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Journal of Mathematical Sciences

, Volume 145, Issue 1, pp 4751–4764 | Cite as

Orbits of subsystem stabilizers

  • N. A. Vavilov
  • N. P. Kharchev
Article
  • 30 Downloads

Abstract

Let Φ be a reduced irreducible root system. We consider pairs (S, X (S)), where S is a closed set of roots, X(S) is its stabilizer in the Weyl group W(Φ). We are interested in such pairs maximal with respect to the following order: (S1, X (S1)) ≤ (S2, X (S2)) if S1 ⊆ S2 and X(S1) ≤ X(S2). The main theorem asserts that if Δ is a root subsystem such that (Δ, X (Δ)) is maximal with respect to the above order, then X (Δ) acts transitively both on the long and short roots in Φ \ Δ. This result is a wide generalization of the transitivity of the Weyl group on roots of a given length. Bibliography: 23 titles.

Keywords

Root System Conjugacy Class Weyl Group Wreath Product Fundamental System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • N. A. Vavilov
    • 1
  • N. P. Kharchev
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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