#10744: Add Demazure character for elements in WeightRing and plotting for rank
2
root systems
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Reporter: benjaminfjones | Owner: sage-combinat
Type: enhancement | Status: new
Priority: minor | Milestone:
Component: combinatorics | Keywords: demazure, root
system, WeylCharacterRing, WeightRing, plot
Author: Benjamin Jones, Daniel Bump | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Add the following enhancements to the `WeightRingElement` class:
1. `demazure_character` method for computing with Demazure operators in
the `WeightRing`.
2. `plot` method for producing 2d plots of characters for the rank 2 root
systems A2, B2, C2, and G2.
3. `degree` method to match the one in `WeylCharacterRing`. This computes
the dimension of the corresponding module.
== Notes: ==
There is already code to compute with Demazure operators in the Crystals
framework (see `demazure_character` in
[http://www.sagemath.org/doc/reference/sage/categories/classical_crystals.html
ClassicalCrystals]). The code provided here lets one work directly in the
`WeightRing`.
Suggestions for making the `plot` method more flexible would be
appreciated. At the moment one can plot the roots and weights together, or
just the weights alone. One can change the root (arrow) style, the weight
(point) style, and the way that weight multiplicities are represented by
point size.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10744>
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