Content deleted Content added
→Demazure modules: definition |
m Correcting spelling: lenght->length |
||
Line 8:
A Demazure module is the ''b''-submodule of ''V'' generated by the weight space of an extremal vector ''w''λ, so the Demazure submodules of ''V'' are parametrized by the Weyl group ''W''.
There are two extreme cases: if ''w'' is trivial the Demazure module is just 1-dimensional, and if ''w'' is the element of maximal
Demazure modules can be defined in a similar way for highest weight representations of [[Kac–Moody algebra]]s, except that one now has 2 cases as one can consider the submodules generated by either the Borel subalgebra ''b'' or its opposite subalgebra. In the finite dimensional these are exchanged by the longest element of the Weyl group, but this is no longer the case in infinite dimensions as there is no longest element.
| |||