Timeline for Irreducible representations of Sp(2)
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2020 at 21:29 | comment | added | wonderich | Isn't Sp(2) as the same as Spin(5)? | |
| Jul 7, 2016 at 8:29 | comment | added | fretty | Then again, it may just be that I am being silly and magma can do exactly what I want! | |
| Jul 7, 2016 at 8:22 | comment | added | fretty | Thanks David, this was actually my initial issue. I am trying to compute the action of Hecke operators on algebraic forms for such a group (well...over an extension of $\mathbb{Q}$). A trace formula exists but it isn't practical (already for $T_{\langle 2 \rangle}$ one has to compute roughly $2.5$ million character values). For "small" weight it seems more plausible to find the space of forms directly and calculate the action explicitly (there are only say $85$ Hecke representatives for $T_{\langle 2 \rangle}$). My main issue is in setting up the representation so that magma lets me act. | |
| Jul 6, 2016 at 9:42 | comment | added | David Loeffler | If you just want any old realisation of the representation that you can do computations with, then you could try using the built-in functionality in Magma for computing explicit models of Lie group representations: see magma.maths.usyd.edu.au/magma/handbook/text/1195#13319. (The chief difficulty I've found in working with this is that it's a pain to construct elements of Lie groups in Magma; e.g. there is no direct way to pass from a 2x2 matrix to a GrpLieElt representing an element of GL(2).) | |
| Jul 5, 2016 at 20:57 | answer | added | 314159. | timeline score: 6 | |
| Jun 20, 2016 at 17:17 | comment | added | fretty | I am not after representations of the Lie algebra since I don't know (explicitly/computationally) how to go from the Lie group to the Lie algebra. Is there a simple answer to my question? Is the representation with Young diagram $(a,b)$ given by homogeneous polynomials in some number of variables that are harmonic with respect to some differential operator? | |
| Jun 20, 2016 at 16:16 | comment | added | Friedrich Knop | What about the advice given in mathoverflow.net/questions/141024/…? | |
| Jun 20, 2016 at 15:20 | comment | added | fretty | I have seen this mentioned but could you explain what the irreducible representations of Spin(5) are? | |
| Jun 20, 2016 at 14:51 | comment | added | Theo Johnson-Freyd | Sp(2) also goes by the name Spin(5). | |
| Jun 20, 2016 at 14:50 | comment | added | fretty | Yes, I wish to know about complex representations. As for explicit, I simply mean any vector space I can generate and compute the action of $\text{Sp}(2)$ on, e.g. spaces of harmonic polynomials. | |
| Jun 20, 2016 at 14:48 | comment | added | Friedrich Knop | Are you talking about complex representations? Also, please make precise what you mean by "explicit description". There are many descriptions around of varying degrees of explicitness (standard monomial theory, crystal bases, LS-paths etc.). There are also a realizations as harmonic polynomials. | |
| Jun 20, 2016 at 14:02 | history | asked | fretty | CC BY-SA 3.0 |