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nLab > Latest Changes: integer Heisenberg group

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTime4 days ago

    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

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTime3 days ago

    have now beautified a little more and added more text.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTime2 days ago

    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.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTime2 days ago
    • (edited 1 day ago)

    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.

1 to 4 of 4

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