Timeline for tannakian description of vector bundles
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2017 at 17:54 | comment | added | Qiaochu Yuan | @ამუკა ჯიბლაძე: vector bundles on $BGL_n$ correspond to finite-dimensional representations of $GL_n$. | |
| Mar 25, 2017 at 23:00 | comment | added | jojo | Hi, thanks for your answer. I have to admit I was hoping for something slightly more explicit. In fact I believe that Remy's comment might be the closest to what I wanted that is possible to get. | |
| Mar 25, 2017 at 20:01 | comment | added | მამუკა ჯიბლაძე | Oops sorry it is an equivalence - more or less by definition. Let me still leave that comment, just in case :D | |
| Mar 25, 2017 at 19:48 | comment | added | მამუკა ჯიბლაძე | One more thing I don't understand (sorry), from the topological perspective. Certainly a representation $GL_n\to GL(V)$ induces $BGL_n\to BGL(V)$, hence a vector bundle on $BGL_n$. But I don't quite see how to go back. Given $BGL_n\to BGL(V)$ one produces $GL_n\to\Omega BGL(V)$ which is not quite $GL(V)$: there is a map $GL(V)\to\Omega BGL(V)$ but I believe it is not an equivalence. | |
| Mar 25, 2017 at 19:46 | comment | added | მამუკა ჯიბლაძე | If $QC(BGL_n)$ can be identified with $Rep(GL_n)$, what kind of representations correspond to the subcategory of $QC(BGL_n)$ consisting of vector bundles? | |
| Mar 25, 2017 at 17:03 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |