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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2013
    • (edited Nov 16th 2013)

    gave representation theory a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over BG\mathbf{B}G and added the following homotopy type representation theory – table, which I am also including in other relevant entries:

    homotopy type theory representation theory
    pointed connected context BG\mathbf{B}G ∞-group GG
    dependent type ∞-action/∞-representation
    dependent sum along BG*\mathbf{B}G \to \ast coinvariants/homotopy quotient
    context extension along BG*\mathbf{B}G \to \ast trivial representation
    dependent product along BG*\mathbf{B}G \to \ast homotopy invariants/∞-group cohomology
    dependent sum along BGBH\mathbf{B}G \to \mathbf{B}H induced representation
    context extension along BGBH\mathbf{B}G \to \mathbf{B}H
    dependent product along BGBH\mathbf{B}G \to \mathbf{B}H coinduced representation
    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 22nd 2013

    Relevant material happening at the nCafe here.

  1. fixed a very tiny typo: , -> .

    anqurvanillapy

    diff, v26, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 19th 2019
    • (edited Jan 19th 2019)

    added pointer to

    • Klaus Lux, Herbert Pahlings, Representations of groups – A computational approach, Cambridge University Press 2010 (author page, publisher page)

    diff, v27, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2021

    added pointer to:

    diff, v33, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 28th 2022
    • (edited Jan 28th 2022)

    for when the editing functionality is back: the entry representation theory should have a pointer to:

  2. added textbook

    Quinn

    diff, v37, current

    • CommentRowNumber8.
    • CommentAuthorAli Caglayan
    • CommentTime1 day ago

    What is the relation with “representation theory in HoTT” and representation theory? I’m sure I could work out the details if I sat down, but reading the article it doesn’t really give a clear link. It would be good if that section was linked back with better understood concepts.

  3. What do you understand by “representation theory”? The standard theory of group actions on vector spaces? One would think linear HoTT best suited for that.

    • CommentRowNumber10.
    • CommentAuthorAli Caglayan
    • CommentTime1 day ago

    Right, what you would usually learn in a first course on representation theory. How exactly does linear HoTT help here? My understanding is that linear HoTT comes from linear logic. Is there a connection there to linear algebra?

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTime18 hours ago

    Yes. For exposition try from slide 16 on here (view in full-screen mode) or the discussion here.