Timeline for Questions about $\mathbb{C}[G/U^-]$ and $\mathbb{C}[B]$

6 events

when toggle format	what		by	license	comment
Sep 6, 2015 at 21:53	answer	added	Christopher Drupieski		timeline score: 4
Sep 6, 2015 at 18:28	answer	added	Ben Webster♦		timeline score: 7
Sep 6, 2015 at 14:05	comment	added	David E Speyer		I have the vague memory there is a statement like this involving Verma modules? Trying to guess what it could be: Maybe, as a $B$-rep, $\mathbb{C}[B] = \bigoplus_{\lambda \in \mathfrak{h}^{\ast}} M_{\lambda}^{\ast}$, where $M_{\lambda}$ is the Verma module. And then $\mathbb{C}[G/U^{-1}] \cap M_{\lambda}^{\ast}$ is $V_{\lambda}^{\ast}$ for $\lambda$ dominant and $0$ otherwise? @BenWebster you are the person whom I usually ask stuff like this. Is anything like my memory right?
Sep 6, 2015 at 3:02	comment	added	Ben Webster♦		What does $V_\lambda^*$ for $\lambda$ not dominant mean?
Sep 6, 2015 at 3:02	comment	added	Allen Knutson		Why should $\mathbb C[B]$ be a $G$-representation? And what would $V_\lambda$ mean if $\lambda$ isn't dominant? As yet, this question is nonsensical. It is true that $B$ embeds as a dense set in $G/U^-$, so $\mathbb C[B]$ contains $\mathbb C[G/U^-]$. Maybe you should say what you mean in the $G=SL_2$ case.
Sep 6, 2015 at 2:16	history	asked	Jianrong Li	CC BY-SA 3.0