nthiery / harmonic-modules

Research notes shared with François Bergeron about computing characters of certain modules of harmonics

Computing the bicharacter of diagonal harmonic polynomials

The main goal of this project is to compute the character of diagonal harmonic polynomials on $k$ rows of $n$ variables w.r.t. the action of $GL_k$ and $S_n$. See DiagonalCharacter.ipynb for explanations, as well as those slides of a talk on the topic (slow to start, but then you can play with the examples live!).

Dependencies: the SageMath open source mathematical system

License: GPL

## Subspace computation facilities

The code for this project includes generic facilities for computing subspaces of general Sage vector spaces like polynomial rings. See utilities.pyx, matrix_of_vectors.py, subspace.py.

This code is being extracted and refactored as a dedicated Sage package, to be eventually integrated into Sage:

https://github.com/darijgr/sage-subspace/

Don't edit the corresponding files in this repo; it will soon go away in favor of using sage-subspace.