Timeline for Decomposition of the ring of functions on the unipotent radical of a Borel
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2012 at 19:41 | comment | added | Alexander Braverman | Look at Kostant's paper that I mentioned above - he does exactly what you want for the $U$-invariants in $k[U]_C$. | |
| Feb 16, 2012 at 16:13 | comment | added | Chuck Hague | (cont'd) In the case of $SL_2$, the construction of Kumar shows that each standard module for $G$ (which in this case is just characterized by its dimension) occurs naturally as a $U$-submodule of $k[U]_L$. I would like to know if something equally nice happens for $k[U]_C$. | |
| Feb 16, 2012 at 16:11 | comment | added | Chuck Hague | Thanks for the comments; perhaps this is another way of stating my question: The structure of $k[U]_L$ as a $U$-module can be fruitfully analyzed by a construction involving $G$-modules, so can a similar thing be done to understand $k[U]_C$? In fact the paper of Joseph that I link to above shows that $k[U]_L$ even has the structure of a module for the hyperalgebra of $G$ compatible with the $U$-module structure (the dual zero Verma structure), although I don't expect such a thing occurs for $k[U]_C$. (cont'd) | |
| Feb 16, 2012 at 13:26 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
added 399 characters in body
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| Feb 15, 2012 at 23:12 | history | answered | Jim Humphreys | CC BY-SA 3.0 |