Timeline for Are plethories a theory of basis-free polynomials?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 28, 2011 at 13:01 | history | edited | Jacques Carette | CC BY-SA 3.0 |
clarify question
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| Oct 28, 2011 at 8:09 | comment | added | Bruce Westbury | The Grothendieck ring of finite dimensional representations of $SL(2)$ is isomorphic to the polynomial ring. The monomial basis is given by taking tensor powers of the fundamental representation. A more natural basis are the irreducible representations (which happen to be the symmetric powers of the fundamental representation). The irreducible representations then correspond to the Chebychev polynomials; so this example, which you mention, is studied. | |
| Oct 28, 2011 at 7:06 | comment | added | Andrew Stacey | I'm unclear as to what you would want to be able to do with a basis-free description of polynomials. My inner category theorist wants to know what you would consider to be the morphisms between spaces of polynomials - if there are any: my experience (which isn't much) is that we tend to think of spaces of polynomials one at a time, whereas we work with lots of vector spaces at the same time. Plethories are more like rings: the right way to move between them is via bimodules. If that's the sort of thing you want, then maybe they are the right description for you. | |
| Oct 28, 2011 at 1:52 | history | edited | Jacques Carette |
fix tag
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| Oct 27, 2011 at 23:37 | comment | added | Gjergji Zaimi | There is a tag "polynomials" already in use... | |
| Oct 27, 2011 at 23:14 | answer | added | Qiaochu Yuan | timeline score: 5 | |
| Oct 27, 2011 at 22:59 | comment | added | Jacques Carette | @Jim: there were not real tags, until now... I welcome suggestions on that front. | |
| Oct 27, 2011 at 22:21 | comment | added | Jim Humphreys | Is "plethory" a real tag? Or "polynomial" for that matter? Too many tags to keep track of. | |
| Oct 27, 2011 at 22:07 | history | asked | Jacques Carette | CC BY-SA 3.0 |