#12914: Representation theory of finite semigroups
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Reporter: nthiery | Owner: tbd
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-5.1
Component: PLEASE CHANGE | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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Add support for representation theory of finite semigroups. Quite some
stuff is available in the sage-combinat queue.
* Required discussions about the current features:
* What to merge now ; what to merge later
* How to specify an indexing of the J-classes
* Should JTrivial / ... be adjectives?
* Should representation theory questions be asked to the semigroup or its
algebra?
* S.character_ring(QQ, ZZ) or S.algebra(QQ).character_ring(ZZ) ?
* S.simple_modules(QQ) or S.algebra(QQ).simple_modules()?
* Character rings
* Should this be called Character ring?
* How to specify the two base rings (for the representations / for the
character ring)?
* Should left and right characters live in the same space (with
realizations)?
e.g.:
* Should there be coercions or conversions between the basis of left-
class modules and right-class modules?
* Should the basis of simple modules on the left and on the right be
identified?
* How to handle subspaces (like for projective modules when the Cartan
matrix is not invertible)
* If we discover that a semigroup is J-trivial, how to propagate this
information to its algebra, character ring, ...?
* Features that remain to be implemented:
* is_r_trivial + _test_r_trivial and friends
* Group of a regular J-class
* Character table for any monoid
* Cartan matrix for any monoid
* Group of a non regular J-class
* Cartan matrix by J-classes
* Radical filtration of a module
* Recursive construction of a triangular basis of the radical
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12914>
Sage <http://www.sagemath.org>
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