Timeline for Fake degrees: why coinvariant algebra and classical groups over finite fields?
Current License: CC BY-SA 4.0
4 events
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| Aug 19, 2019 at 10:05 | comment | added | David E Speyer | @LSpice This is the standard meaning of "coinvariant algebra" in invariant theory. See eg math.uchicago.edu/~margalit/repthy/lecturesRT.pdf . It is unfortunate that it is not what happens if you apply the definition of "coinvariant" ncatlab.org/nlab/show/coinvariant to an algebra, but such is human language. | |
| Aug 19, 2019 at 8:46 | comment | added | kneidell | I know very little on this subject, but I think your question may be answered in Carter's Finite groups of Lie type book, Ch 10-12. The key factor, as far as I understand, in seeing this connection is the (non-trivial) isomorphism between $\mathbb C[W]$ and the Hecke algebra $\mathbb C[B\backslash G/B]$, and the notion of specialisation, which gives representation dimensions in the former case and fake degrees in the latter. | |
| Aug 19, 2019 at 5:21 | comment | added | LSpice | Is your definition of "co-invariant algebra" the usual one? I am used to the term meaning the largest quotient (instead of the largest subobject) on which $\mathrm S_n$ acts trivially, namely, the quotient of $R$ by the ideal generated by $(1 - \sigma)r$ with $\sigma \in \mathrm S_n$ and $r \in R$. | |
| Aug 19, 2019 at 4:06 | history | asked | Sam Hopkins | CC BY-SA 4.0 |