#8442: Lie Methods and Related Combinatorics (tutorial)
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Reporter: bump | Owner: bump
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.6.1
Component: documentation | Keywords:
Author: Daniel Bump | Upstream: N/A
Reviewer: Minh Van Nguyen, Mark Jordan | Merged:
Work_issues: |
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Comment(by dimpase):
Replying to [comment:45 bump]:
> > It would also be good if anything is said regarding the optional Sage
package lie (by Marc van Leeuween). Is it right that basically anything
doable in lie can be done in Sage? In particular, lie can compute
decompositions of, say, a tensor product of two representations into
irreducibles. It's not clear to me whether one can do this in Sage
(without lie).
>
> I am not sure whether everything that is doable with LiE is doable with
Sage but I do think that anything that is needed from LiE is either in
Sage already or (if needed) should be reimplemented. What is in Sage is a
pretty complete toolkit for finite-dimensional representations of Lie
groups. Decomposing a tensor product into irreducibles is just the
multiplication in the WeylCharacterRing. This is addressed in the
tutorial. See:
>
> http://match.stanford.edu/bump/thematic_tutorials-
js/lie/weyl_character_ring.html#tensor-products-of-representations
One particular thing I was able to do using Lie was to compute things in
classical invariant theory, such as the dimension of the space of
invariants of degree k
of the m-ary form of degree d (for fixed k,m,d). Basically, that meant
computing certain symmetric power of certain representation of GL_m (or
SL_m), and finding out whether there was a 1-dimensional sub-
representation.
Is this doable in Sage?
Thanks!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8442#comment:46>
Sage <http://www.sagemath.org>
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