Timeline for Decomposing a polynomial ring into Specht Modules
Current License: CC BY-SA 4.0
14 events
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| May 14, 2020 at 10:29 | comment | added | Mark Wildon | I don't know of anything that I'm confident will help you. Semistandard homomorphisms have been generalised to Hecke algebras. I think this is Mathas' book and another version is in a paper of Lyle: arxiv.org/abs/1101.3192. The extra 'rigidity' in Hecke algebras might perhaps help with the non-canonicity you mention. Just for the record, my notes ma.rhul.ac.uk/~uvah099/Maths/doubleRevised2.pdf have some relevant ideas. (This is of course known to you: thank you darij for your many helpful corrections.) | |
| May 14, 2020 at 10:22 | comment | added | darij grinberg | I might have asked already, but: has there been any more modern exposition of semistandard homomorphisms than in James's LNM booklet? I've tried a couple times to generalize them to pictures, and each times I've gotten lost in the forest of non-canonical identifications that at least the definition in James seems to get into. | |
| May 14, 2020 at 10:21 | history | edited | darij grinberg | CC BY-SA 4.0 |
added 21 characters in body
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| May 14, 2020 at 8:48 | history | edited | Mark Wildon | CC BY-SA 4.0 |
Correction to Spechtian determinant
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| May 14, 2020 at 8:47 | comment | added | Mark Wildon | I've corrected the determinant: it comes from the standard tableaux of shape (n-3,2,1) with first column $1,2,3$ and second column $4,5$. For example, expanding both on the main diagonal gives $x_2x_3^2x_5$ which is a monomial of the right 'shape'. | |
| May 14, 2020 at 4:39 | comment | added | Karthik C | Thanks so so much Mark, specially for reminnding me of the Kostka numbers, I should have known that! The $M_{(n-3,2,1)}$ just occurred to me this morning and I was on the right track! | |
| May 14, 2020 at 4:31 | comment | added | Karthik C | Also, should that determinant not be $\det\begin{vmatrix}1&1&1\\x_1&x_2&x_3\\x_1^2&x_2^2&x_3^2\end{vmatrix}x_i$? where $i=1,2,3$? | |
| May 14, 2020 at 4:23 | vote | accept | Karthik C | ||
| May 13, 2020 at 17:03 | history | edited | Mark Wildon | CC BY-SA 4.0 |
edited body
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| May 13, 2020 at 16:40 | history | undeleted | Mark Wildon | ||
| May 13, 2020 at 16:40 | history | edited | Mark Wildon | CC BY-SA 4.0 |
Big correction: I missed that the degree was general, not 4
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| May 13, 2020 at 16:17 | history | deleted | Mark Wildon | via Vote | |
| May 13, 2020 at 16:15 | history | edited | Mark Wildon | CC BY-SA 4.0 |
added 86 characters in body
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| May 13, 2020 at 16:05 | history | answered | Mark Wildon | CC BY-SA 4.0 |