Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2013
   • (edited Nov 16th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexgave _[[representation theory]]_ a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over $\mathbf{B}G$ 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]] $\mathbf{B}G$ | [[∞-group]] $G$ | | [[dependent type]] | [[∞-action]]/[[∞-representation]] | | [[dependent sum]] along $\mathbf{B}G \to \ast$ | [[coinvariants]]/[[homotopy quotient]] | | [[context extension]] along $\mathbf{B}G \to \ast$ | [[trivial representation]] | | [[dependent product]] along $\mathbf{B}G \to \ast$ | [[homotopy invariants]]/[[∞-group cohomology]] | [[dependent sum]] along $\mathbf{B}G \to \mathbf{B}H$ | [[induced representation]] | | [[context extension]] along $\mathbf{B}G \to \mathbf{B}H$ | | | [[dependent product]] along $\mathbf{B}G \to \mathbf{B}H$ | [[coinduced representation]]

   gave representation theory a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over $\mathbf{B}G$ 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 $\mathbf{B}G$	∞-group $G$
   dependent type	∞-action/∞-representation
   dependent sum along $\mathbf{B}G \to \ast$	coinvariants/homotopy quotient
   context extension along $\mathbf{B}G \to \ast$	trivial representation
   dependent product along $\mathbf{B}G \to \ast$	homotopy invariants/∞-group cohomology
   dependent sum along $\mathbf{B}G \to \mathbf{B}H$	induced representation
   context extension along $\mathbf{B}G \to \mathbf{B}H$
   dependent product along $\mathbf{B}G \to \mathbf{B}H$	coinduced representation

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 22nd 2013
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexRelevant material happening at the nCafe [here](http://golem.ph.utexas.edu/category/2013/12/commuting_limits_and_colimits.html#c045379).

   Relevant material happening at the nCafe here.

3. • CommentRowNumber3.
   • CommentAuthornLab edit announcer
   • CommentTimeNov 28th 2018
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexfixed a very tiny typo: , -> . anqurvanillapy <a href="https://ncatlab.org/nlab/revision/diff/representation+theory/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/representation+theory/26">v26</a>, <a href="https://ncatlab.org/nlab/show/representation+theory">current</a>

   fixed a very tiny typo: , -> .

   anqurvanillapy

   diff, v26, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2019
   • (edited Jan 19th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * Klaus Lux, Herbert Pahlings, _Representations of groups -- A computational approach_, Cambridge University Press 2010 ([author page](http://www.math.rwth-aachen.de/~RepresentationsOfGroups/), [publisher page](http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521768078)) <a href="https://ncatlab.org/nlab/revision/diff/representation+theory/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/representation+theory/27">v27</a>, <a href="https://ncatlab.org/nlab/show/representation+theory">current</a>

   added pointer to

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

   diff, v27, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 6th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Tammo tom Dieck]], [[Theodor Bröcker]], *Representations of compact Lie groups*, Springer 1985 ([doi:10.1007/978-3-662-12918-0](https://link.springer.com/book/10.1007/978-3-662-12918-0)) <a href="https://ncatlab.org/nlab/revision/diff/representation+theory/33">diff</a>, <a href="https://ncatlab.org/nlab/revision/representation+theory/33">v33</a>, <a href="https://ncatlab.org/nlab/show/representation+theory">current</a>

   added pointer to:

   • Tammo tom Dieck, Theodor Bröcker, Representations of compact Lie groups, Springer 1985 (doi:10.1007/978-3-662-12918-0)

   diff, v33, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJan 28th 2022
   • (edited Jan 28th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexfor when the editing functionality is back: the entry *[[representation theory]]* should have a pointer to: * [[Jean-Pierre Serre]], *Linear Representations of Finite Groups*, Springer 1977 ([doi:10.1007/978-1-4684-9458-7](https://doi.org/10.1007/978-1-4684-9458-7))

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

   • Jean-Pierre Serre, Linear Representations of Finite Groups, Springer 1977 (doi:10.1007/978-1-4684-9458-7)
7. • CommentRowNumber7.
   • CommentAuthornLab edit announcer
   • CommentTimeJul 10th 2023
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadded textbook * [[Peter Woit]], *Quantum Theory, Groups and Representations: An Introduction*, Springer 2017 &lbrack;[doi:10.1007/978-3-319-64612-1](https://doi.org/10.1007/978-3-319-64612-1), ISBN:978-3-319-64610-7&rbrack; Quinn <a href="https://ncatlab.org/nlab/revision/diff/representation+theory/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/representation+theory/37">v37</a>, <a href="https://ncatlab.org/nlab/show/representation+theory">current</a>

   added textbook

   • Peter Woit, Quantum Theory, Groups and Representations: An Introduction, Springer 2017 [doi:10.1007/978-3-319-64612-1, ISBN:978-3-319-64610-7]

   Quinn

   diff, v37, current

8. • CommentRowNumber8.
   • CommentAuthorAli Caglayan
   • CommentTimeMay 24th 2024
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexWhat 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.

   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.

9. • CommentRowNumber9.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 24th 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexWhat do you understand by "representation theory"? The standard theory of group actions on vector spaces? One would think linear HoTT best suited for that.

   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.

10. • CommentRowNumber10.
    • CommentAuthorAli Caglayan
    • CommentTimeMay 24th 2024
    • PermaLink
    Author: Ali Caglayan
    Format: MarkdownItexRight, 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?

    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?

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexYes. For exposition try from slide 16 on [here](https://ncatlab.org/schreiber/files/Schreiber-ToposInstitute-230417.pdf) (view in full-screen mode) or the discussion [here](https://ncatlab.org/schreiber/show/Towards+Quantum+Programming+via+Linear+Homotopy+Types#QuantumViaLinearHomotopyTypes).

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

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 10th 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Pavel Etingof]], Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, [[Dmitry Vaintrob]], Elena Yudovina: *Introduction to representation theory*, Student Mathematical Library **59**, AMS (2011) &lbrack;[arXiv:0901.0827](https://arxiv.org/abs/0901.0827), [ams:stml-59](https://bookstore.ams.org/stml-59)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/representation+theory/39">diff</a>, <a href="https://ncatlab.org/nlab/revision/representation+theory/39">v39</a>, <a href="https://ncatlab.org/nlab/show/representation+theory">current</a>

    added pointer to:

    • Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, Elena Yudovina: Introduction to representation theory, Student Mathematical Library 59, AMS (2011) [arXiv:0901.0827, ams:stml-59]

    diff, v39, current