#15536: Implement symplectic and orthogonal bases of Sym
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: combinatorics | Resolution:
Keywords: days54, sym | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/combinat/sf/sp_orth | 57f92dd1a206bb5af2ed00e4135ded0c586e99db
Dependencies: #17096 | Stopgaps:
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Comment (by zabrocki):
Travis, thanks for pointing this out to me. The `st` basis in ticket
#19327 is very similar and since the group of permutation matrices are
orthogonal matrices, it will be that `o(lambda)` has a positive `st`
expansion.
There is an explicit formula for the change of basis from `sp` and `o` to
Schur basis (that is almost exactly the same as the `_s_to_sp_on_basis`
and `_s_to_o_on_basis` that you have implemented, it just alternates in
sign by degree and the set of partitions you sum over are transposed). Is
it faster to use the triangularity like you have here? Are you aware of
it and have you tried it?
--
Ticket URL: <http://trac.sagemath.org/ticket/15536#comment:21>
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