Opened 4 years ago

Last modified 4 years ago

#18665 new enhancement

Add verbose method names for primitive central and seminormal idempotents

Reported by: s.r.doty Owned by:
Priority: trivial Milestone: sage-6.8
Component: combinatorics Keywords: days65, symmetric group algebra, idempotents
Cc: s.r.doty, sage-combinat, saliola, zabrocki, virmaux, nthiery Merged in:
Authors: Stephen Doty Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

The SymmetricGroupAlgebra? class has methods (cpi, cpis, and epsilon_ik whose names do not advertise their function. These should be renamed to something more appropriate. For example,

cpi = central_primitive_idempotent
cpis = central_primitive_idempotents
epsilon_ik = seminormal_basis_element

Also, there should be a separate function for seminormal_idempotent which is the equivalent of running epsilon_ik with both input tableaux the same. I.e., this new function should return the seminormal idemotent indexed by a given standard tableau.

Change History (3)

comment:1 Changed 4 years ago by saliola

  • Cc virmaux nthiery added

comment:2 Changed 4 years ago by nthiery

Just wondering: shouldn't this be primitive central idempotents? It's about the central idempotents that are primitive, not about primitive idempotents that are central.

For the record: for good or bad, in SemisimpleAlgebras.FiniteDimensional, the method computing those is called central_orthogonal_idempotents. Consistency one way or the other would be nice!

comment:3 Changed 4 years ago by virmaux

Maybe we could just overload the SemisimpleAlgebras.FiniteDimensional method with cpi by renaming this last one, as it may be faster.

sage: A4 = SymmetricGroup(4).algebra(QQ)
sage: A4.central_orthogonal_idempotents() == A4.cpis()
True
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