Opened 5 years ago

Closed 4 years ago

#23037 closed enhancement (fixed)

Implement representations for Virasoro algebra

Reported by: tscrim Owned by:
Priority: major Milestone: sage-8.2
Component: algebra Keywords: lie algebras
Cc: sage-combinat, darij Merged in:
Authors: Travis Scrimshaw Reviewers: Frédéric Chapoton
Report Upstream: N/A Work issues:
Branch: 999dcfb (Commits, GitHub, GitLab) Commit: 999dcfba45b3b896f74aaa63f2300fde6532f7d4
Dependencies: Stopgaps:

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Description (last modified by tscrim)

We implement the chargeless representations and Verma modules for the Virasoro algebra. Along the way, we also add witt to the catalog and change the bracket convention for the Witt and Virasoro algebras.

A note on the change to the bracket convention: Our current bracket convention is non-standard with the rest of the literature and causes formulas to change in subtle ways. So the easiest thing to do is change it, and I think this will be better in the long run.

Change History (19)

comment:1 Changed 5 years ago by tscrim

  • Branch set to public/lie_algebras/reprs_virasoro-23037
  • Commit set to 8069b1838180e4c3aac306d8ac93af1f88efb21b
  • Status changed from new to needs_review

New commits:

65a57d4Improving doc and check for (p)Witt algebras.
e614c79Fixed __mul__ for Lie algebra elements to handle actions.
c7a49c4Implement chargeless represenation.
8069b18Changing bracket convention for Witt and Virasoro. Implementing Verma modules.

comment:2 Changed 5 years ago by git

  • Commit changed from 8069b1838180e4c3aac306d8ac93af1f88efb21b to aaeb1c9a7258a17d66391260ed05d299360ebfaf

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

aaeb1c9Updating documentation.

comment:3 Changed 4 years ago by git

  • Commit changed from aaeb1c9a7258a17d66391260ed05d299360ebfaf to 4c17c8cbaac586a2c085acf273da19e61829028f

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

4c17c8cMerge branch 'public/lie_algebras/reprs_virasoro-23037' of git://trac.sagemath.org/sage into public/lie_algebras/reprs_virasoro-23037

comment:4 Changed 4 years ago by chapoton

There is one it.next that should be next(it) for py3 sake, no ?

and doc does not build, probably because of

+    this for `\{d_i \mid -10 \leq i < 10\}::

EDIT: typo "+ REFERNCES::"

Last edited 4 years ago by chapoton (previous) (diff)

comment:5 Changed 4 years ago by git

  • Commit changed from 4c17c8cbaac586a2c085acf273da19e61829028f to 2fdd3e46baa3ac120646c86d0edbdc4701ad8c6f

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

2fdd3e4Use next() and typo fixes.

comment:6 Changed 4 years ago by tscrim

Yes, thanks. Fixed.

comment:7 Changed 4 years ago by chapoton

another issue here:

+    REFERENCES::

has too many colons

comment:8 Changed 4 years ago by git

  • Commit changed from 2fdd3e46baa3ac120646c86d0edbdc4701ad8c6f to 4b9ef9413c64d2c081977d1266b24e451d7d5aa7

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

4b9ef94No double colon on references.

comment:9 Changed 4 years ago by tscrim

Good catch. Fixed.

comment:10 Changed 4 years ago by tscrim

  • Description modified (diff)

comment:11 follow-up: Changed 4 years ago by chapoton

A strange sentence here in Verma modules:

+    The Virasoro algebra admits a triangle decomposition of

Maybe you mean of the shape ?

Otherwise, looks good.

comment:12 Changed 4 years ago by git

  • Commit changed from 4b9ef9413c64d2c081977d1266b24e451d7d5aa7 to 8dfb361968ed8d631bdd8f5ede5387e7fb7a1500

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

8dfb361Tweak documentation.

comment:13 in reply to: ↑ 11 Changed 4 years ago by tscrim

  • Milestone changed from sage-8.0 to sage-8.2

Replying to chapoton:

A strange sentence here in Verma modules:

+    The Virasoro algebra admits a triangle decomposition of

Maybe you mean of the shape ?

No, it is a triangular decomposition in the same way of simple Lie algebras or Lie groups by the root system (positive, negative, and 0 parts). I made some tweaks to the documentation; they probably don't help much, but maybe they do.

Otherwise, looks good.

Thank you very much for looking at this.

Last edited 4 years ago by tscrim (previous) (diff)

comment:14 Changed 4 years ago by chapoton

I understand the triangular decomposition, sure.

You introduced a typo : "trianglar"

I would simply remove the "of"

comment:15 Changed 4 years ago by git

  • Commit changed from 8dfb361968ed8d631bdd8f5ede5387e7fb7a1500 to 999dcfba45b3b896f74aaa63f2300fde6532f7d4

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

999dcfbFixes in virasoro.VermaModule.

comment:16 Changed 4 years ago by tscrim

Ah, sorry, I misunderstood your comment:11. Here is the fix from comment:14.

comment:17 Changed 4 years ago by chapoton

  • Reviewers set to Frédéric Chapoton
  • Status changed from needs_review to positive_review

Thanks. Then good to go.

comment:18 Changed 4 years ago by tscrim

Thank you again very much for the review!

comment:19 Changed 4 years ago by vbraun

  • Branch changed from public/lie_algebras/reprs_virasoro-23037 to 999dcfba45b3b896f74aaa63f2300fde6532f7d4
  • Resolution set to fixed
  • Status changed from positive_review to closed
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