#19327: Symmetric group characters as bases of the symmetric functions
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Reporter: zabrocki | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: combinatorics | Keywords: sf, sage-combinat
Merged in: | Authors: Mike Zabrocki
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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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.
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Ticket URL: <http://trac.sagemath.org/ticket/19327>
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