Ticket #9290 (new enhancement)

Opened 3 years ago

Last modified 6 months ago

Implement Coxeter groups in their geometric representation

Reported by: nthiery Owned by: sage-combinat
Priority: major Milestone: sage-wishlist
Component: combinatorics Keywords: coxeter
Cc: sage-combinat Work issues:
Report Upstream: N/A Reviewers:
Authors: Merged in:
Dependencies: Stopgaps:

Description (last modified by nthiery) (diff)

The root system / coxeter group code is designed from the ground up to allow for this extension.

Steps:

  • Double check CartanType(["H",3]).coxeter_diagram() and friends
  • Given a coxeter diagram, construct the dynkin diagram g corresponding to the geometric representation; most of the time, this will involve roots of unity, and require e.g. a cyclotomic field (see also #8327)
  • Make sure that L = RootSystem(g).root_space() accepts such a diagram
  • Make sure that WeylGroup(L) accepts such a root space
  • Fix all the interfaces to properly reflect the generalization (e.g. WeylGroup? above should really be CoxeterGroup?).

Change History

comment:1 Changed 3 years ago by nthiery

Partially depends on #8237

comment:2 Changed 3 years ago by nthiery

  • Description modified (diff)

comment:3 Changed 6 months ago by chapoton

  • Keywords coxeter added
Note: See TracTickets for help on using tickets.