Infinity crystal of tableaux

[bsalisbury1]

Implements infinity crystal of tableaux in types A, B, C, D, and G.

Apply: trac_14192-infinity_crystal-bs.patch​

[tscrim]

I've uploaded a small review patch which makes some small tweaks/fixes to the documentation.

[aschilling]

Hi Ben and Travis,

Thanks for your work on this. Here are a couple of comments:

• Could you please fold the two patches? That makes it easier to review!

• In the title "\mathcal{B}(\infty) Crystals of Tableaux" specify the types for which this works.

• There are trailing white spaces. Please remove them!

• Why don't you put the Element class into the parent class (by indentation)? See for example how this is done in Littelmann paths. Also, the parent class should come first!

• In string_parameters, the Examples are indented wrongly!

Please make these changes and then I'll look again!

Anne

[bsalisbury1]

Folded in review. Made appropriate changes.

For patchbot:

Apply: trac_14192-infinity_crystal-bs.patch

[aschilling]

Thanks for making the changes! Could you also move the patch past 14143 in the sage-combinat queue and make the appropriate rebases there? 14252 is almost ready to go in as well, so we can make a dependence either way for that patch (but I think 14143 needs a little longer due to the plot patch it depends on).

Thanks!

Anne

[bsalisbury1]

Made it so this does not depend on #14252 and #14252 (in the combinat queue) did not have any dependency on this patch (at least there was no fuzz that Travis and I saw).

For patchbot:

Apply trac_14192-infinity_crystal-bs.patch

[aschilling]

Replying to bsalisbury1:

Made it so this does not depend on #14252 and #14252 (in the combinat queue) did not have any dependency on this patch (at least there was no fuzz that Travis and I saw).

For patchbot:

Apply trac_14192-infinity_crystal-bs.patch

Did you get this backwards? There should *not* be a dependency on 14143, but rather on 14252?

[tscrim]

Yes...We typed in the wrong patch numbers. This does depend on #14252 and not on #14143.

For patchbot:

Apply: trac_14192-infinity_crystal-bs.patch

[aschilling]

Hi!

The patch needs to be exported properly. Currently the header says

# HG changeset patch # Parent b75f7b88f08e78885465bdf7149a1995337342c2

• * *

#14192: Review patch for infinity crystal of tableaux.

Anne

[aschilling]

Hi Ben and Travis,

Here are some further comments:

• The reference [KN94] seems to be missing in the documentation. It is not clickable.

• Since you mention "... in the i-th row from the top i" you need to clarify whether you are using English or French conventions for the tableaux.

• Please say something about the shape of the tableaux you are using. I assume they can be arbitrarily large.

• Too many "the" in "...the the i-th row"

• The reference [BN10] D. Bump and M. Nakasuji. Integration on p-adic groups and crystal bases. Proc. Amer. Math. Soc. 138(5), pp. 1595–1605. is not referred to.

• The input I assume is a finite Cartan type. Please specify this in "cartan_type – A Cartan type".

• In the doctest for f you say "Return the action of e˜i on self." I guess this should be f~!

• In the doc for reduced_form, the following is not a sentence: "The reduced form of a T∈(∞) that is a tableaux with all i-boxes in the i-th row removed and if the row is empty, a ∗ is put as a placeholder." Perhaps you want to remove the "that"?

• In the documentation for string_parameters, please define the boldface i.

• In the definition of weight, there are two typos in "indendepent of the path choosen". Also, please say that the \alpha_i are simple roots.

• In InfinityCrystalOfTableauxTypeD replace "constaints" by "constraints".

So much for now!

Anne

[aschilling]

I have another suggestion, which would be good to have as a test for the implementation. Could you program the projection to B(\lambda) (at least in a few examples) to check that the result is indeed isomorphic to a highest weight crystal?

Anne

[bsalisbury1]

Fixed.

[aschilling]

I commuted 14192 past 14252 in the sage-combinat queue to get rid of the dependency. Please get the newest version of the patch from there! Could you please post the new version here? Then I think it is close to getting a positive review.

Anne

[aschilling]

There are still trailing white spaces in the patch (in several places in infinite_crystal.py). Please remove them!

Anne

[bsalisbury1]

Removed trailing whitespace (hopefully).

[aschilling]

Looks good!