Timeline for Questions about $\mathbb{C}[G/U^-]$ and $\mathbb{C}[B]$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 11, 2016 at 15:31 | comment | added | Jim Humphreys | @ L Spice: The article is more-or-less available online: gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002436086 | |
| S Dec 11, 2016 at 14:27 | history | suggested | LSpice | CC BY-SA 3.0 |
Lowest -> longest weight vectors; added link to reference
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| Dec 11, 2016 at 14:10 | comment | added | LSpice | I changed the reference to account for @WilberdvanderKallen's correction. | |
| Dec 11, 2016 at 14:10 | review | Suggested edits | |||
| S Dec 11, 2016 at 14:27 | |||||
| Sep 9, 2015 at 14:28 | comment | added | Jianrong Li | @Wilberd van der Kallen, thank you very much. | |
| Sep 9, 2015 at 9:45 | comment | added | Wilberd van der Kallen | One must use the action on $\mathbb C[B]$ from the left and from the right. Filter by requiring that weights are no further than $d$ from zero for both actions. That is, look at maximal submodules (for the double action) with that property. This gives a canonical filtration which one should make explicit in terms of the coordinates. You should find multiplicities for $d$ less than 5. | |
| Sep 9, 2015 at 9:37 | comment | added | Jianrong Li | @Wilberd van der Kallen, thank you very much. In $SL_2$ case, how can we show that there is multiplicity of $V^*_{\lambda}$ in $\mathbb{C}[B]$? Do we have $\mathbb{C}[B] = \bigoplus_{\lambda} M_{\lambda}^*$, where $M_{\lambda}$ is a Verma module with highest weight $\lambda$? | |
| Sep 7, 2015 at 11:24 | comment | added | Wilberd van der Kallen | The P(−λ) are the $V(λ)^*$ of Jianrong Li, so there must be multiplicities. It must already be visible for $SL_2$ that there are multiplicities so that the map $\bigoplus_{h\in S} M_\lambda^* \to \mathbb{C}[B]$ is not surjective. | |
| Sep 7, 2015 at 7:23 | comment | added | Wilberd van der Kallen | The paper was about longest weight vectors, not just lowest weight vectors. | |
| Sep 6, 2015 at 21:53 | history | answered | Christopher Drupieski | CC BY-SA 3.0 |