#15806: Integrable representations of (affine) Kac-Moody Lie Algebras
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Reporter: bump | Owner: bump
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: Kac-Moody | Merged in:
Authors: bump | Reviewers:
Report Upstream: N/A | Work issues:
Branch: public/combinat/integrable- | Commit:
representations-15806 | Stopgaps:
Dependencies: |
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Changes (by bump):
* commit: 3f9a71760d30fd170bdb40f192cf4e5b6af73bab =>
* branch: u/bump/combinat/integrable-representations-15806 =>
public/combinat/integrable-representations-15806
Old description:
> Integrable representations of Kac-Moody Lie algebras are parametrized by
> dominant weights. They satisfy a character formula which is a
> straightforward generalization of the Weyl character formula. See Kac,
> Infinite-dimensional Lie algebras, Chapter 10. The affine case is an
> important special case that was developed in connection with string
> theory. Since (in this affine case) generating functions for the weight
> dimensions may be modular forms there are all sorts of connections and it
> would be good to have this in Sage. It should be straighforward to write
> such code, and that is the purpose of this ticket.
> The workhorse algorithm will be the Freudenthal multiplicity formula.
>
> I am unsure at this point whether to implement only the affine case or
> the general Kac-Moody case.
New description:
Integrable representations of Kac-Moody Lie algebras are parametrized by
dominant weights. They satisfy a character formula which is a
straightforward generalization of the Weyl character formula. See Kac,
Infinite-dimensional Lie algebras, Chapter 10. The weight multiplicities
may be computed using the Freudenthal multiplicity formula, and Kass,
Moody, Patera and Slansky in their book Affine Lie algebras, weight
multiplicities, and branching rules (1990) gave tables of these for affine
Lie algebras. We may duplicate their tables using Sage, though at the
moment only untwisted type A is implemented.
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Ticket URL: <http://trac.sagemath.org/ticket/15806#comment:11>
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