Opened 5 years ago

Last modified 5 years ago

#18000 new enhancement

Root multiplicities for symmetrizable Kac-Moody algebras

Reported by: jonathan.judge Owned by: jonathan.judge
Priority: major Milestone: sage-6.8
Component: combinatorics Keywords: days64
Cc: bump, bsalisbury1, khlee Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: u/jonathan.judge/root_multiplicities_for_symmetrizable_kac_moody_algebras (Commits) Commit: 55d2f5269995e5ee42fbe765f657721257bf0c57
Dependencies: #18644, #18645 Stopgaps:

Description

Add a method (probably in root_lattice_realizations) to compute the multiplicity of a given root. The algorithm is the Peterson recursive formula.

Change History (5)

comment:1 Changed 5 years ago by jonathan.judge

  • Branch set to u/jonathan.judge/root_multiplicities_for_symmetrizable_kac_moody_algebras

comment:2 Changed 5 years ago by jonathan.judge

  • Commit set to 4958ee0f2ebf0fe63dec7231b3111f2a4dd1d63d
  • Owner changed from (none) to jonathan.judge

New commits:

4958ee0Added a function multiplicity() on elements of a root lattice. The computation is done via Peterson's recurrent formula

comment:3 Changed 5 years ago by jonathan.judge

  • Dependencies set to 18644, 18645
  • Milestone changed from sage-6.6 to sage-6.8

comment:4 Changed 5 years ago by jonathan.judge

  • Dependencies changed from 18644, 18645 to #18644, #18645

comment:5 Changed 5 years ago by git

  • Commit changed from 4958ee0f2ebf0fe63dec7231b3111f2a4dd1d63d to 55d2f5269995e5ee42fbe765f657721257bf0c57

Branch pushed to git repo; I updated commit sha1. New commits:

d700a67Merge branch 'develop' into t/18000/root_multiplicities_for_symmetrizable_kac_moody_algebras
77f1bf6Added methods is_indefinite(), is_hyperbolic(), is_indecomposable(), and principal_submatrices() to the class CartanMatrix
2560229Merge branch 't/18645/add_some_methods_to_cartanmatrix' into t/18000/root_multiplicities_for_symmetrizable_kac_moody_algebras
c7a1b37Fixed element method is_real_root() in root_lattice_realizations.py
3cc6587Merge branch 't/18645/add_some_methods_to_cartanmatrix' into t/18644/fix_method_is_real_root___in_root_lattice_realizations_py
6784229Merge branch 't/18644/fix_method_is_real_root___in_root_lattice_realizations_py' into t/18000/root_multiplicities_for_symmetrizable_kac_moody_algebras
55d2f52Rewrote multiplicity computation to take advantage of new and corrected methods in 18644 and 18645
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