#15375: Extended Affine Weyl Groups SD40
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Reporter: bump | Owner: bump
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: days54, coxeter, | Merged in:
days64, days65 | Reviewers: Dan Bump, Anne
Authors: Daniel Bump, Dan | Schilling
Orr, Anne Schilling, Mark | Work issues:
Shimozono, Nicolas Thiery. | Commit:
Report Upstream: N/A | b9152e2bc08cd314744b5fd5ef627a467778f25a
Branch: | Stopgaps:
public/combinat/extended_affine_weyl_groups-15375|
Dependencies: #10963, #14102 |
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Comment (by mshimo):
Nicolas, Thanks very much for your comments.
I need to know the reason behind using {{{cartan_type.special_node()}}}.
Let's call this the extra special node. For simplicity we assume untwisted
affine type. By deletion we obtain a subsystem of finite type.
If the extra special node is nonzero then the correct behavior is that
the "classical subsystem" should be a relabeling of the
appropriate standard classical subsystem
with 0 as one of the "finite" Dynkin nodes.
This nonstandard classical Dynkin node set will get propagated to
indices of simple roots and fundamental weights and to the
finite Weyl groups. In particular we could see
t_{\omega_0^\vee} as a nontrivial translation element
and s_0 as an element of the finite Weyl group.
Do we really want this?
--Mark
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Ticket URL: <http://trac.sagemath.org/ticket/15375#comment:77>
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