#19327: Symmetric group characters as bases of the symmetric functions
-------------------------------------+-------------------------------------
Reporter: zabrocki | Owner:
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-6.10
Component: combinatorics | Resolution:
Keywords: sf, sage-combinat | Merged in:
Authors: Mike Zabrocki | Reviewers: Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/combinat/sf/character_bases-19327|
84f5917bbf3ffa4d7fc04b1abe2220e8871060b9
Dependencies: #15536 | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by zabrocki):
* status: needs_review => positive_review
Old description:
> This ticket implements two inhomogeneous bases of the symmetric
> functions, one called the `irreducible_character` and the other
> `induced_trivial_character` and shorthands `st` and `ht`. These bases
> play the roll for the symmetric group realized as permutation matrices
> that the Schur functions play to the character of the irreducible Gl_n
> representations.
>
> In addition, two methods are added to the symmetric function element
> class. One `eval_at_permutation_roots` that evaluates a symmetric
> function at the roots of unity of a permutation matrix with a given cycle
> type and the other, `eval_at_permutation_roots`, interprets a symmetric
> function as a symmetric group character and computes the Frobenius image.
New description:
This ticket implements two inhomogeneous bases of the symmetric functions,
one called the `irreducible_character` and the other
`induced_trivial_character` and shorthands `st` and `ht`. These bases
play the roll for the symmetric group realized as permutation matrices
that the Schur functions play to the character of the irreducible Gl_n
representations.
In addition, two methods are added to the symmetric function element
class. One `eval_at_permutation_roots` that evaluates a symmetric
function at the roots of unity of a permutation matrix with a given cycle
type and the other, `character_to_frobenius_image`, interprets a symmetric
function as a symmetric group character and computes the Frobenius image.
--
Comment:
I've checked that all tests pass.
--
Ticket URL: <http://trac.sagemath.org/ticket/19327#comment:23>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
