Opened 11 years ago

Last modified 11 years ago

#10744 new enhancement

Add Demazure character for elements in WeightRing and plotting for rank 2 root systems

Reported by: benjaminfjones Owned by: sage-combinat
Priority: minor Milestone:
Component: combinatorics Keywords: demazure, root system, WeylCharacterRing, WeightRing, plot
Cc: bump, aschilling, nthiery Merged in:
Authors: Benjamin Jones Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

Add the following enhancements to the WeightRingElement class:

  1. demazure_character method for computing with Demazure operators in the WeightRing.
  1. plot method for producing 2d plots of characters for the rank 2 root systems A2, B2, C2, and G2.
  1. 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 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.

Attachments (2)

trac_10744_demazure_plot.patch (13.3 KB) - added by benjaminfjones 11 years ago.
trac_10744_demazure_plot_v2.patch (17.8 KB) - added by benjaminfjones 11 years ago.

Download all attachments as: .zip

Change History (4)

Changed 11 years ago by benjaminfjones

comment:1 Changed 11 years ago by benjaminfjones

  • Authors changed from Benjamin Jones, Daniel Bump to Benjamin Jones

comment:2 Changed 11 years ago by benjaminfjones

I'm uploading a new patch (version 2) which addresses suggestions from the sage-combinat-devel list. The changes are:

  1. added doctests for the _demazure helper method
  2. many enhancements to plot incuding:
    1. plotting the weight lattice
    2. plotting the dominant Weyl chamber
    3. turned plotting the axes off by default

The plots produced by the four examples in the docstring for plot can be viewed here:

https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_1.png https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_2.png https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_3.png https://bluedrive.uwstout.edu/users/facultystaff/jonesbe/research/sage/ex_4.png

Changed 11 years ago by benjaminfjones

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