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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTime3 days ago
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting an entry on the integer Heisenberg group. For the moment it remains telegraphic as far as the text is concerned (no Idea-section) but it contains a slick (I find) computation of the modular transformation of Chern-Simons/WZW states from the manifest modular automorphy of certain integer Heisenberg groups. Hope to beautify this entry a little more tomorrow (but won't have much time, being on an intercontinental flight) or else the days after (where I am however at a conference, but we'll see). <a href="https://ncatlab.org/nlab/revision/integer+Heisenberg+group/1">v1</a>, <a href="https://ncatlab.org/nlab/show/integer+Heisenberg+group">current</a>

   starting an entry on the integer Heisenberg group.

   For the moment it remains telegraphic as far as the text is concerned (no Idea-section)

   but it contains a slick (I find) computation of the modular transformation of Chern-Simons/WZW states from the manifest modular automorphy of certain integer Heisenberg groups.

   Hope to beautify this entry a little more tomorrow (but won’t have much time, being on an intercontinental flight) or else the days after (where I am however at a conference, but we’ll see).

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTime2 days ago
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave now beautified a little more and added more text. <a href="https://ncatlab.org/nlab/revision/diff/integer+Heisenberg+group/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/integer+Heisenberg+group/2">v2</a>, <a href="https://ncatlab.org/nlab/show/integer+Heisenberg+group">current</a>

   have now beautified a little more and added more text.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTime2 days ago
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI don't have time but there might be connections to Ganter's categorical tori, in how she contracts the crossed module from a lattice that is the kernel of exp, and a central extension.

   I don’t have time but there might be connections to Ganter’s categorical tori, in how she contracts the crossed module from a lattice that is the kernel of exp, and a central extension.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTime1 day ago
   • (edited 19 hours ago)
   • PermaLink
   Author: Urs
   Format: MarkdownItexNot sure what specifically you are thinking of? Maybe I can amplify that the mere existence of the integer/discrete Heisenberg group is immediate and classical. The point that I meant to record here is that its evident action by the modular group (which is still obvious) induces a modular action on its irrep which is the famous modular functor of abelian Chern-Simons theory that is no longer that obvious and traditionally derived only over pages of analysis of geometric quantization. This is an observation which I have not seen discussed anywhere. But since its proof is so elementary (as recorded in the entry), I won't be surprised if this has been noted somewhere before. A reference would be welcome.

   Not sure what specifically you are thinking of?

   Maybe I can amplify that the mere existence of the integer/discrete Heisenberg group is immediate and classical. The point that I meant to record here is that its evident action by the modular group (which is still obvious) induces a modular action on its irrep which is the famous modular functor of abelian Chern-Simons theory that is no longer that obvious and traditionally derived only over pages of analysis of geometric quantization.

   This is an observation which I have not seen discussed anywhere. But since its proof is so elementary (as recorded in the entry), I won’t be surprised if this has been noted somewhere before. A reference would be welcome.