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

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Sep 7, 2015 at 12:39	comment	added	Ben Webster♦		@VítTuček The description in the original posting. This wasn't explicitly said, but if you follow the argument through, the isomorphism $\mathbb C[G/U_-]\cong \oplus_{\lambda}V_{\lambda}^*$ is given by the functions $f_x$ for $x$ in $V_{\lambda}$.
Sep 6, 2015 at 20:21	comment	added	Vít Tuček		So $\lambda$ runs through all possible weights and the isomorphism $\bigoplus_{h\in S} M_\lambda^* \to \mathbb{C}[B]$ is an isomorphism of $B$-modules? How do you make the connection to $G/U_{-}$?
Sep 6, 2015 at 18:39	comment	added	Ben Webster♦		@DavidSpeyer Those aren't quite the conventions I used, but up to some minus signs, yes.
Sep 6, 2015 at 18:38	history	edited	Ben Webster♦	CC BY-SA 3.0	added 299 characters in body
Sep 6, 2015 at 18:32	comment	added	David E Speyer		Thanks Ben! And, just for the record, the maximal finite dimensional subrep of $M_{\lambda}^{\ast}$ is $V_{\lambda}^{\ast}$ if $\lambda$ is dominant, and $0$ otherwise, right?
Sep 6, 2015 at 18:28	history	answered	Ben Webster♦	CC BY-SA 3.0