Improvements to Lie theory documentation

[tscrim]

Add some newer features and results into the Lie theory documentation. This also fixes typos, formatting, and flow.

CC: @sagetrac-sage-combinat @anneschilling @dwbump

Component: documentation

Keywords: sd58

Author: Travis Scrimshaw

Branch/Commit: c8f5e49

Reviewer: Dan Bump

Issue created by migration from https://trac.sagemath.org/ticket/16498

[tscrim]

New commits:

94deba2

Various changes, fixed, additions, and improvements to Lie theory.

[tscrim]

Changed keywords from none to sd58

[tscrim]

Branch: public/doc/lie_tutorial_cleanup-16498

[tscrim]

Commit: 94deba2

[dwbump]

comment:2

The changes are noncontroversial but there is a doctest failure in affine_hw_crystals.rst:

File "affine_hw_crystals.rst", line 92, in doc.en.thematic_tutorials.lie.affine_hw_crystals
Failed example:
    CM = CartanMatrix([[2, -1, -1,-1],[-1,2,-1,-1],[-1,-1,2,-1],[-1,-1,-1,2]]); M
Exception raised:
[snip]
    NameError: name 'M' is not defined

[dwbump]

Reviewer: bump

[sagetrac-git]

Changed commit from 94deba2 to ef88d2a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f994469	Merge branch 'public/doc/lie_tutorial_cleanup-16498' of trac.sagemath.org:sage into pulbic/doc/lie_tutorial_cleanup-16498
ef88d2a	Fixed trivial typo with doctest.

[tscrim]

Changed reviewer from bump to Dan Bump

[tscrim]

comment:5

Whoops, fixed (and it's now based on 6.3.beta4). Is there anything you want added/expanded upon in here Dan?

[dwbump]

comment:6

I think there are further things that should be in the thematic tutorial but they don't have to go in this patch. For example, the methods of root lattice and weight lattice realizations for affine case.
It is best that this be a separate patch because the changes here are noncontroversial and presumably can be merged quickly.

[anneschilling]

comment:8

There is a typo in the single KR crystal section:

vertify -> verify

Also, since you mention projections, it should be mentioned which projection (onto what) gives the KR crystals.

[sagetrac-git]

Changed commit from ef88d2a to c8f5e49

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

c8f5e49

Fixed typo and added projection image for level 0 crystals.

[tscrim]

comment:10

Fixed and done. If you're happy with the change, please set this back to positive review.

[vbraun]

Changed branch from public/doc/lie_tutorial_cleanup-16498 to c8f5e49