#19327: Symmetric group characters as bases of the symmetric functions
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Reporter: zabrocki | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: sf, sage-combinat | Merged in:
Authors: Mike Zabrocki | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/zabrocki/sf/characterbases/19327 | 0d0ad367e18486002e0ec1dd36899b31f840aa38
Dependencies: #17096 | Stopgaps:
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Changes (by zabrocki):
* status: needs_review => needs_work
* dependencies: => #17096
Comment:
This basis is similar to those found in #15536. In fact the orthogonal
basis will have a positive expansion in the
`irreducible_symmetric_group_character` basis (because permutation
matrices are orthogonal). As a result I've added the filtered algebras
ticket as a dependency. I checked and these bases also have an antipode
problem and probably suffer from the same counit issue that the `sp` and
`o` bases had at the start.
I merged #17096 into this branch on my computer and compilings starting
failing. Given that I am on OSX 10.11 and Xcode 7 this means trouble for
me because I have been in a precarious situation where compiling sage from
scratch makes it unusable.
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Ticket URL: <http://trac.sagemath.org/ticket/19327#comment:8>
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