#12774: various enhancements for Coxeter and Weyl groups
---------------------------------------------+------------------------------
Reporter: mshimo | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: combinatorics | Resolution:
Keywords: coxeter group, weyl group | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Mark Shimozono | Merged in:
Dependencies: #6588, #12667 | Stopgaps:
---------------------------------------------+------------------------------
Changes (by mshimo):
* cc: sage-combinat-devel (added)
* status: new => needs_review
Old description:
> Various enhancements to Coxeter groups and Weyl groups.
>
> 1. Computes inversions for Coxeter and Weyl groups. They occur in three
> forms: reflections, roots, and coroots.
>
> New Coxeter group element methods:[[BR]]
> categories/coxeter_groups.py
>
> apply_conjugation_by_simple_reflection [[BR]]
> length_decreasing_reflections_right [[BR]]
> length_decreasing_reflections_left [[BR]]
>
> New Weyl group element methods: [[BR]]
> categories/weyl_groups.py
>
> reflection_to_root [[BR]]
> reflection_to_coroot [[BR]]
> inversions [[BR]]
>
> New root space element method: [[BR]]
> combinat/root_system/root_space.py
>
> associated_reflection
>
>
> Bruhat covering relations have an associated inversion. Accordingly,
> we have added versions of the Coxeter group element methods
> bruhat_lower_covers and bruhat_upper_covers which incorporate the
> inversion data:
>
> New Coxeter group element methods:[[BR]]
> categories/coxeter_groups.py
>
> bruhat_cocovers_reflections[[BR]]
> bruhat_covers_reflections[[BR]]
>
> New Weyl group element methods:[[BR]]
> categories/weyl_groups.py
>
> bruhat_cocovers_coroots[[BR]]
> bruhat_covers_coroots[[BR]]
>
> 2. Installs the Demazure or 0-Hecke product for Coxeter groups
>
> New Coxeter group parent method:[[BR]]
> categories/coxeter_groups.py[[BR]]
>
> demazure_product
>
> New Coxeter group element methods:[[BR]]
> categories/coxeter_groups.py
>
> apply_demazure_simple_reflection[[BR]]
> apply_demazure_product[[BR]]
> min_demazure_product_greater[[BR]]
>
> 3. Computes canonical lifts from quotients by parabolic subgroups.
> This requires Deodhar's recovery of the Bruhat order on a Coxeter group
> from that on a parabolic subgroup and the quotient by that subgroup.
>
> New Coxeter group element methods:[[BR]]
> categories/coxeter_groups.py
>
> deodhar_factor_element[[BR]]
> deodhar_lift_up[[BR]]
> deodhar_lift_down[[BR]]
>
> 4. Two random little methods for root systems
>
> sage/combinat/root_system/root_lattice_realizations.py:[[BR]]
> new parent method:[[BR]]
> positive_roots_by_height[[BR]]
>
> sage/combinat/root_system/root_space.py:[[BR]]
> new element method:[[BR]]
> max_coroot_le
New description:
Various enhancements to Coxeter groups and Weyl groups.
1. Computes inversions for Coxeter and Weyl groups. They occur in three
forms: reflections, roots, and coroots.
New Coxeter group element methods:[[BR]]
categories/coxeter_groups.py
apply_conjugation_by_simple_reflection [[BR]]
inversions_as_reflections
left_inversions_as_reflections
New Weyl group element methods: [[BR]]
categories/weyl_groups.py
reflection_to_root [[BR]]
reflection_to_coroot [[BR]]
inversions [[BR]]
New root space element method: [[BR]]
combinat/root_system/root_space.py
associated_reflection
Bruhat covering relations have an associated inversion. Accordingly,
we have added versions of the Coxeter group element methods
bruhat_lower_covers and bruhat_upper_covers which incorporate the
inversion data:
New Coxeter group element methods:[[BR]]
categories/coxeter_groups.py
bruhat_cocovers_reflections[[BR]]
bruhat_covers_reflections[[BR]]
New Weyl group element methods:[[BR]]
categories/weyl_groups.py
bruhat_cocovers_coroots[[BR]]
bruhat_covers_coroots[[BR]]
2. Installs the Demazure or 0-Hecke product for Coxeter groups
New Coxeter group parent method:[[BR]]
categories/coxeter_groups.py[[BR]]
demazure_product
New Coxeter group element methods:[[BR]]
categories/coxeter_groups.py
apply_demazure_simple_reflection[[BR]]
apply_demazure_product[[BR]]
min_demazure_product_greater[[BR]]
3. Computes canonical lifts from quotients by parabolic subgroups.
This requires Deodhar's recovery of the Bruhat order on a Coxeter group
from that on a parabolic subgroup and the quotient by that subgroup.
New Coxeter group element methods:[[BR]]
categories/coxeter_groups.py
deodhar_factor_element[[BR]]
deodhar_lift_up[[BR]]
deodhar_lift_down[[BR]]
4. Small changes for root systems
sage/combinat/root_system/root_lattice_realizations.py:[[BR]]
new parent method:[[BR]]
positive_roots_by_height[[BR]]
modified the calling convention for weyl_action
sage/combinat/root_system/root_space.py:[[BR]]
new element method:[[BR]]
max_coroot_le
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12774#comment:2>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
