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]

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

]]>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?

]]>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.

]]>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.

]]>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

]]>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)

added pointer to:

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

added pointer to

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

fixed a very tiny typo: , -> .

anqurvanillapy

]]>Relevant material happening at the nCafe here.

]]>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 |