We establish for which parabolic subgroups P of a simply connected and semisimple algebraic group G with unipotent radical U and Levi factor H the two rings k[G/H]U and k[U^−] are isomorphic as H algebras. We show the relation of this problem with a Theorem of Schmid and we compare the multiplications in the rings k[U^−] and k[G/H].
On a theorem of Schmid
ESPOSITO, FRANCESCO;
2008
Abstract
We establish for which parabolic subgroups P of a simply connected and semisimple algebraic group G with unipotent radical U and Levi factor H the two rings k[G/H]U and k[U^−] are isomorphic as H algebras. We show the relation of this problem with a Theorem of Schmid and we compare the multiplications in the rings k[U^−] and k[G/H].
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