Changes between Initial Version and Version 1 of Ticket #14085


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Timestamp:
02/09/13 02:08:44 (7 years ago)
Author:
nthiery
Comment:

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  • Ticket #14085

    • Property Summary changed from Implement ambient spaces for dual and affine root systems to Ambient spaces for dual and affine root systems
  • Ticket #14085 – Description

    initial v1  
     1This ticket implements ambient spaces for dual and affine root
     2systems. So now all finite and affine crystallographic root systems
     3have an ambient space, except for relabeled ones (to be handled in a
     4separate ticket).
     5
     6Upcoming applications:
     7
     8* Plotting #4237
     9* Affine permutation representations built from the ambient space
     10* Macdonald polynomials
     11* Affine weight ring (in waiting for #7922 for weight rings built from
     12  the root or weight lattice)
     13
     14A couple things handled by this patch:
     15- Fixing a couple whitespaces
     16- Standard color scheme (to be used by #4237)
     17- Fundamental weights computed from simple roots (finite type)
     18- Better handling of the smallest base ring for the ambient space
     19  (toward ambient spaces over fields/rings like RR)
     20- Better handling of dual types: in particular make sure the dual
     21  CartanType belongs to the appropriate CartanType classes; this
     22  allowed to remove now unnecessary code.
     23- Fix the embedding of the root lattice into the extended weight
     24  lattice for type BC dual. A Type free approach would be better.