Opened 6 years ago

Last modified 6 years ago

#20420 new enhancement

Implement dual braid monoids/groups and Hecke algebras for complex reflection groups

Reported by: tscrim Owned by: sage-combinat
Priority: major Milestone: sage-7.2
Component: combinatorics Keywords:
Cc: sage-combinat, stumpc5, vripoll Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
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Description

Using the non-crossing partition lattice, we can implement a Garside structure for dual braid monoids and groups for (well-generated) Complex reflection groups. Moreover, we can use this to implement the Hecke algebras.

Change History (2)

comment:1 Changed 6 years ago by stumpc5

Here is a first trivial way of getting a (non-reduced) presentation for the dual braid monoid:

sage: W = ReflectionGroup(24); W.is_well_generated()
True
sage: NC = W.noncrossing_partition_lattice()
sage: X = W.reflections().inverse_family()
sage: for chain in NC.maximal_chains():^J    print [ X[chain[i-1].inverse()*chain[i]] for i in range(1,len(chain)) ]

For whatever reason, here is the documentation of Hecke algebras in Chevie: https://webusers.imj-prg.fr/~jean.michel/gap3/htm/chap082.htm

comment:2 Changed 6 years ago by vripoll

  • Cc vripoll added
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