Timeline for How to write $\mathbb{C}[G/U_-]=\oplus_{\lambda} V_{\lambda}$ explicitly?

5 events

when toggle format	what		by	license	comment
May 3, 2016 at 14:41	answer	added	Allen Knutson		timeline score: 7
May 3, 2016 at 8:06	vote	accept	Jianrong Li
May 3, 2016 at 6:54	answer	added	Friedrich Knop		timeline score: 12
May 3, 2016 at 3:40	comment	added	Dave Witte Morris		It is not true that $G = U_- B$ (unless $n = 1$, I guess). The set $U_- B$ is dense and open, but it is only the "big cell" of the Bruhat decomposition, and there are other (lower-dimensional) cells that are needed to get all of $G$. However, you are right that there is an embedding $\mathbb{C}[G/U_-] \hookrightarrow \mathbb{C}[B]$. (In your example, don't you also need the functions $g_{22}$, $g_{23}$, and $g_{33}$?)
May 3, 2016 at 3:28	history	asked	Jianrong Li	CC BY-SA 3.0