Opened 7 years ago

Closed 7 years ago

#14085 closed enhancement (fixed)

Ambient spaces for dual and affine root systems

Reported by: nthiery Owned by: sage-combinat
Priority: major Milestone: sage-5.8
Component: combinatorics Keywords:
Cc: sage-combinat, tscrim, mshimo, aschilling Merged in: sage-5.8.beta2
Authors: Nicolas M. Thiéry Reviewers: Dan Orr, Anne Schilling
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by nthiery)

This ticket implements ambient spaces for dual and affine root systems. So now all finite and affine crystallographic root systems have an ambient space, except for relabeled ones (to be handled in a separate ticket).

Upcoming applications:

  • Plotting #4237
  • Affine permutation representations built from the ambient space
  • Macdonald polynomials
  • Affine weight ring (in waiting for #7922 for weight rings built from the root or weight lattice)

A couple things handled by this patch:

  • Fixing a couple whitespaces
  • Standard color scheme (to be used by #4237)
  • Fundamental weights computed from simple roots (finite type)
  • Better handling of the smallest base ring for the ambient space (toward ambient spaces over fields/rings like RR)
  • Better handling of dual types: in particular make sure the dual CartanType? belongs to the appropriate CartanType? classes; this allowed to remove now unnecessary code.
  • Fix the embedding of the root lattice into the extended weight lattice for type BC dual. A Type free approach would be better.
  • Prevent affine crystals to use the ambient space, even if available, for backward compatibility. This may be changed in a later ticket.
  • Implement to_simple_root, and generalizes associated_reflection for every root lattice realizations using it
  • More tests for the null (co)root.
  • Improved section about ambient spaces in the introduction to root systems. Includes the link with (affine/signed) permutation representations.
  • Improved doc for the delta notation glitch for extended weight lattice realizations.
  • Various documentation improvements.

Attachments (1)

trac_14085-root_system-ambient_spaces-nt.patch (84.3 KB) - added by nthiery 7 years ago.

Download all attachments as: .zip

Change History (11)

comment:1 Changed 7 years ago by nthiery

  • Description modified (diff)
  • Summary changed from Implement ambient spaces for dual and affine root systems to Ambient spaces for dual and affine root systems

comment:2 Changed 7 years ago by nthiery

  • Status changed from new to needs_review

comment:3 Changed 7 years ago by nthiery

  • Status changed from needs_review to needs_work

comment:4 Changed 7 years ago by nthiery

  • Description modified (diff)
  • Status changed from needs_work to needs_review

comment:5 Changed 7 years ago by tscrim

  • Cc tscrim added

comment:6 Changed 7 years ago by nthiery

The updated patch fixes two minor doctests failures I had missed and that the patchbot reported. I assume that the third failure in interface/expect.py is unrelated.

Cheers,

Nicolas

comment:7 Changed 7 years ago by nthiery

  • Description modified (diff)

comment:8 Changed 7 years ago by nthiery

  • Cc mshimo aschilling added

New version with quite a few improvements. Unless I missed something, I consider this patch as final. Please review!

comment:9 Changed 7 years ago by nthiery

  • Reviewers changed from Dan Orr, ... to Dan Orr, Anne Schilling
  • Status changed from needs_review to positive_review

Anne reviewed this patch on the Sage-Combinat queue. The updated patch includes her changes which were cross checked by Nicolas. We also discussed further the math with Mark Shimozono.

Positive review!

Anne and Nicolas

comment:10 Changed 7 years ago by jdemeyer

  • Merged in set to sage-5.8.beta2
  • Resolution set to fixed
  • Status changed from positive_review to closed
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