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Stephen J. Watson
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You could say that the Lusztig data is parameterizing basis vectors in a hw representation.
(Oh I see Dan beat me to it...)
How do you know that intertwiners respect your decomposition into Lusztig data in general?
Might that be a type A phenomenon?
I think Kirillov has such a paper…
Aren't there Gelfan Tsetlin patters for Orthogonal groups (B+D) together
@Siddhartha - Yes. Proctor has a J. Algebra paper from the 90’s doing all kinds of branching rules for classical groups.
Can you build a *solvable* lattice model for every reduced decomposition of the longest word?
@Siddhartha Valentin and I know how to do this for type B, but type D seems to be really hard
For the usual character that is
@Benjamin -- Perhaps the orthogonal branching is already due to Gelfand-Tsetlin?
@Siddhartha - I used to attribute to Zhelobenko, but you are probably right.
If Lusztig data parametrize basis vectors, what do colored Lusztig data parametrize?
It is an important question
These decompositions are parametrized by reduced words for the long Weyl group element
In the colored case, do you also obtain vertex states' weight by computing the integrals over the corresponding piece?