Implement Fock space #15508

tscrim · 2013-12-11T06:59:06Z

In type A. I put this in a new algebras/quantum_groups folder in preparation of Lie algebras and quantum groups #14901.

Depends on #25067

CC: @sagetrac-sage-combinat @AndrewAtLarge @anneschilling @bsalisbury1

Component: algebra

Keywords: Fock space quantum group representations

Author: Travis Scrimshaw

Branch/Commit: b4f73fa

Reviewer: Andrew Mathas

Issue created by migration from https://trac.sagemath.org/ticket/15508

The text was updated successfully, but these errors were encountered:

AndrewMathas · 2013-12-11T08:53:22Z

comment:2

Hi Travis,

Thanks for both working on this and for letting me know about it. I just had a quick glance through it and it looks very nice, but there is a lot of code to digest! The fact that the new improved git-world makes it difficult to separate the current ticket from its dependencies makes this harder of course. I will try and look through this properly in due course as it is one of the things that I care about - and implementing this was on my to-do list.

A few questions/comments (based on my very quick read through):

I noticed that you have implemented Fayer's LLT algorithm for computing the canonical bases of the combinatorial Fock spaces. I haven't looked at all at the details of your code but in his paper Fayers' has a conjecture for the degrees of the polynomials that came up (they should always be less than the defect/weight), and he mentioned that if this conjecture were true then there are some shortcuts which speed up his algorithm. Fayers' conjecture is now known to be true, so I was wondering whether you have used this in your code.
Am I right in thinking that you have only implemented the Fock spaces F(\Lambda) such that F(\Lambda)\cong F(\Lambda_{a_1})\otimes\dots\otimes F(\Lambda_{a_k}), for dominant weights \Lambda=\Lambda_{a_1}+\dots+\Lambda_{a_k}?

In addition to these "standard" Fock spaces there are some more general Fock spaces for U_q(\widehat{sl}_e) defined by Uglov. I am asking this more for information/clarification as Uglov's Fock spaces don't come up in my work - they arise in the cateogorification of rational Cherednik algebras.
In terms of displaying the elements of the Fock space I think that

  |[3, 1]> + q*|[2, 2]> + q^ 2*|[2, 1, 1]>

is too cumbersome. I would prefer something like

  |3, 1> + q*|2, 2> + q^ 2*|2, 1, 1>

and something similar for higher levels. Other alternatives would be

  F(3, 1) + q*F(2, 2) + q^ 2*F(2, 1, 1)

or

  F([3, 1]) + q*F([2, 2]) + q^ 2*F([2, 1, 1])

which both have the distinct advantage that you can cut and paste the output back into sage (for a suitably defined shortcut F).

Cheers,
Andrew

tscrim · 2013-12-11T19:37:16Z

comment:3

Hey Andrew,

Replying to @AndrewAtLarge:

Thanks for both working on this and for letting me know about it. I just had a quick glance through it and it looks very nice, but there is a lot of code to digest! The fact that the new improved git-world makes it difficult to separate the current ticket from its dependencies makes this harder of course.

Actually, there's not a functional dependency on #15289, just some syntax, so I can commute this past with relative ease if #15289 doesn't get reviewed before we are done with this.

I will try and look through this properly in due course as it is one of the things that I care about - and implementing this was on my to-do list.

A few questions/comments (based on my very quick read through):

[I]n his paper Fayers' has a conjecture for the degrees of the polynomials that came up (they should always be less than the defect/weight), ... Fayers' conjecture is now known to be true, so I was wondering whether you have used this in your code.

No I do not. Currently I don't check if a partition is regular, so I guess I'm really computing for the full tensor product space. I should also note another abuse; my indexing set for the highest weight modules is too large (I'm using all partitions instead of just the n-regular and giving an error when the user tries to create a non-n-regular partition). I probably should change that...
>.>
<.<

Am I right in thinking that you have only implemented the Fock spaces F(\Lambda) such that F(\Lambda)\cong F(\Lambda_{a_1})\otimes\dots\otimes F(\Lambda_{a_k}), for dominant weights \Lambda=\Lambda_{a_1}+\dots+\Lambda_{a_k}?

Correct.

In addition to these "standard" Fock spaces there are some more general Fock spaces for U_q(\widehat{sl}_e) defined by Uglov. I am asking this more for information/clarification as Uglov's Fock spaces don't come up in my work - they arise in the cateogorification of rational Cherednik algebras.

Hmm...interesting. Do you have a reference I could look at?

In terms of displaying ... I would prefer something like
  |3, 1> + q*|2, 2> + q^ 2*|2, 1, 1>
and something similar for higher levels.

I will make this change along with restricting the indexing set to the proper set.

Best,

Travis

tscrim · 2013-12-27T03:03:44Z

Changed dependencies from #15289 to #15289 #15525

sagetrac-git · 2013-12-27T03:38:39Z

Changed commit from 4548a5b to 1daad96

sagetrac-git · 2013-12-27T03:38:39Z

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

`1daad96`	`Changes to term formatting and restricted some indexing sets.`
`f5a794b`	`Merge branch 'public/combinat/partitions_constraints-15525' into public/modules/fock_space`
`1adb368`	`Added deprecation to IntegerListLex global_options arg. Fixed doctests.`
`2341248`	`Merge branch 'public/combinat/partitions_constraints-15525' into public/modules/fock_space`
`4143c96`	`Merge branch 'develop' into public/combinat/partitions_constraints-15525`
`976a4d1`	`Merge branch 'public/combinat/partitions_constraints-15525' into public/modules/fock_space`
`82d7b6f`	`Merge branch 'master' into public/modules/fock_space`
`7982d3a`	`Iniital fix and added regular partitions.`
`3597354`	`Merge branch 'master' into public/modules/fock_space`

tscrim · 2013-12-27T03:42:24Z

comment:7

I still need to restrict the indices for the general HW representations.

sagetrac-git · 2014-01-02T17:46:51Z

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

`ac31208`	`Fixed indexing set and doctest.`
`2eaee1b`	`Converted to the proper indexing set for HW repr.`
`772c09b`	`Merge branch 'public/combinat/regular_partition_tuples' into public/modules/fock_space`
`12f1d6b`	`Added regular partition tuples.`

sagetrac-git · 2014-01-02T17:46:51Z

Changed commit from 1daad96 to ac31208

sagetrac-git · 2014-01-02T17:57:04Z

Changed commit from ac31208 to 62afb1b

sagetrac-git · 2014-01-02T17:57:04Z

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

`62afb1b`	`Added TODO message for HW repr.`

tscrim · 2014-01-02T17:58:22Z

Changed dependencies from #15289 #15525 to #15289 #15525 #15621

tscrim · 2014-01-02T17:58:22Z

comment:10

What does the Fock say? It goes #15621 and back to needs review. :p

sagetrac-git · 2014-03-04T17:51:03Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`991953a`	`Merge branch 'develop' into public/monoids/15289-indexed`
`b51bc3d`	`Merge branch 'public/monoids/15289-indexed' into public/modules/fock_space`
`f13f9ad`	`Merge branch 'develop' into public/modules/fock_space`
`bd82ed8`	`Merge branch 'develop' into public/monoids/15289-indexed`
`56703eb`	`Made Indexed* have entry points through Free*.`
`163df6e`	`Changed more _basis_keys to _indices, deprecated the former.`
`8db8e0a`	Changed `_an_element_` to indexed_monoid.py.
`760c939`	`Merge branch 'public/monoids/15289-indexed' of trac.sagemath.org:sage into public/monoids/15289-indexed`
`03057a4`	`Merge branch 'develop' into public/monoids/15289-indexed`
`d2f6254`	`Merge branch 'public/monoids/15289-indexed' into public/modules/fock_space`

sagetrac-git · 2014-03-04T17:51:03Z

Changed commit from 62afb1b to d2f6254

sagetrac-git · 2014-03-13T05:25:18Z

Changed commit from d2f6254 to 9fe7ae7

sagetrac-git · 2014-03-13T05:25:18Z

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

`a2996e0`	`Merge branch 'develop' into public/monoids/15289-indexed`
`9fe7ae7`	`Merge branch 'public/monoids/15289-indexed' into public/modules/fock_space`

sagetrac-git · 2017-11-15T11:00:21Z

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

`407c806`	`Merge branch 'public/modules/fock_space' in 8.1.rc0`

sagetrac-git · 2017-11-15T11:00:21Z

Changed commit from c101a33 to 407c806

fchapoton · 2017-11-18T20:56:10Z

comment:64

typo "agianst"
could we "lazy import" this new things ?

sagetrac-git · 2017-11-20T23:03:48Z

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

`8e50781`	`Merge branch 'public/modules/fock_space' of git://trac.sagemath.org/sage into public/modules/fock_space`
`c6aec4a`	`Fixed typo.`

sagetrac-git · 2017-11-20T23:03:48Z

Changed commit from 407c806 to c6aec4a

tscrim · 2017-11-20T23:13:47Z

comment:66

Replying to @fchapoton:

typo "agianst"

Fixed.

could we "lazy import" this new things ?

The only thing added to the global namespace is FockSpace, which is lazily imported. The quantum_groups/all.py file is not, but IMO, that should not be lazily imported (and we do not do that anywhere else).

sagetrac-git · 2018-03-31T11:54:37Z

Changed commit from c6aec4a to a898d44

sagetrac-git · 2018-03-31T11:54:37Z

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

`67c6ba0`	`Adding q-analogs used in quantum groups.`
`a898d44`	`Merge branch 'public/modules/fock_space' of git://trac.sagemath.org/sage into public/modules/fock_space`

tscrim · 2018-03-31T11:55:17Z

comment:68

Trivial rebase having split off the q-numbers to a separate ticket.

tscrim · 2018-03-31T11:55:17Z

Dependencies: #25067

sagetrac-git · 2018-03-31T13:27:24Z

Changed commit from a898d44 to f4bba3e

sagetrac-git · 2018-03-31T13:27:24Z

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

`e908d59`	`Adding q-analogs used in quantum groups.`
`f4bba3e`	`Merge branch 'public/quantum_groups/q_numbers-25067' into public/modules/fock_space`

sagetrac-git · 2018-04-30T06:11:10Z

Changed commit from f4bba3e to b4f73fa

sagetrac-git · 2018-04-30T06:11:10Z

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

`b4f73fa`	`Minor tweaks to documentation`

AndrewMathas · 2018-04-30T06:13:16Z

comment:71

The code looks good. I have made a few minor tweaks to the documentation and changed the hi method to the more descriptive h_inverse. If you are happy with these, and all tests pass, then please consider this a positive review.

tscrim · 2018-04-30T06:13:41Z

Reviewer: Andrew Mathas

tscrim · 2018-04-30T06:14:04Z

comment:73

Thank you very much.

vbraun · 2018-05-14T17:36:11Z

Changed branch from public/modules/fock_space to b4f73fa

tscrim added this to the sage-6.0 milestone Dec 11, 2013

tscrim added c: algebra labels Dec 11, 2013

tscrim assigned sagetrac-sage-combinat Dec 11, 2013

tscrim added the s: needs review label Dec 11, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.0, sage-6.1 Dec 17, 2013

tscrim added s: needs work and removed s: needs review labels Dec 27, 2013

tscrim added s: needs review and removed s: needs work labels Jan 2, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

tscrim added s: needs review and removed s: needs work labels Oct 5, 2017

tscrim modified the milestones: sage-8.1, sage-8.2 Mar 31, 2018

tscrim added s: positive review and removed s: needs review labels Apr 30, 2018

vbraun removed the s: positive review label May 14, 2018

vbraun closed this as completed in e5af488 May 14, 2018

This was referenced Jun 17, 2022

Lie algebras #14901

Open

Implement regular partition tuples #15621

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AndrewMathas mentioned this issue May 18, 2018

KleshchevPartitions #20564

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tscrim mentioned this issue Jan 8, 2023

Implement quantum group q-numbers #25067

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Implement Fock space #15508

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Implement Fock space #15508

Implement Fock space #15508

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