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View Code? Open in Web Editor NEWResearch notes shared with François Bergeron about computing characters of certain modules of harmonics
Research notes shared with François Bergeron about computing characters of certain modules of harmonics
Split the code into following Python modules:
Keep code.py that just loads all the others, so that one can still load everything in the notebook for basic usage.
cc @phubert
The code is entangled because too much is put on the shoulders of DiagonalPolynomialRing
. Instead, we should refine the modelling of the problem and create independent parents and functions:
class DiagonalPolynomialRing:
"""
The ring of diagonal polynomials in n x r variables + n x inert variables
EXAMPLES::
sage: DiagonalPolynomialRing(QQ, n, r, inert=0)
"""
def young_idempotent(self, p, mu):
def polarization(self, p, ...):
...
class DiagonalAntisymmetricPolynomials:
"""
The subspace of diagonal polynomials that are antisymmetric w.r.t. certain variables
Polynomials are represented by picking within each orbit of monomials a canonical one.
"""
def from_polynomial(self, p):
'''Create an element from a fully expanded antisymmetric polynomial'''
def young_idempotent(self, p):
''''''
def polarization()
'''compute usual polarization and renormalize'''
def PolarizationSpace(P, generators, mu, r, use_symmetry=, verbose=, use_lie, use_commutativity???=):
"""
Starting from polynomials in the mu-isotypic component of the polynomial ring in one set of variables (possibly with additional inert variables), construct the space obtained by polarization.
P: a diagonal polynomial ring (or assymmetric version)
generators: polynomials in one set of variables (+inert) in the image of b_mu
"""
def harmonic_XXX(mu, n):
'''construct a basis of the mu-isotypic component of harmonic polynomials in n variables through higher specht polynomials'''
def YYY(mu, nu, n):
'''The analogue for Pauline's case'''
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