极小抛物子代数上具Borel-Weil-Bott性质的权

Weights with the Borel-Weil-Bott Property on the Minimal Parabolie Subalgebras

对支配权引入在极小抛物子代数上具有Borel-Weil-Bott性质的概念.证明了:若λ在极小抛物子代数上具有Borel-Weil-Bott性质,则λ在Uq上Borel-Weil-Bott定理成立.还证明,对如此的λ,有Uq模同构H0q(λ)■H0q(-w0λ)*,且H0q(λ)是首权为λ的不可约Uq模.在chk=0的情形,本文刻画了具有Borel-Weil-Bott性质的正则支配权的特征.作为例子,对A1,A2型量子代数,给出了有足够多的非正则支配权具有Borel-Weil-Bott性质.

This paper introduced a new concept--dominant weight with the Borel - Well - Bott property on the minimal parabolie s ubalgebras. It was proved that if λ has the Borel- Weil- Bott property on the minimal parabolie subalgebras, then A satisfies the Borel- Weil- Bott theory on Uq and that for such A there is the Uq module isomorphism Hq^0 （λ） ≈ Hq^0 （ - w0 λ ）＊ , where Hq^0 （λ） is a irreducible Uq module with the highest weight A . At the case chk = 0 , the charaterization of the l - regular dominant weight with the Borel- Weil- Bott property was described. As an example, for the quantum algebras of type A1 ,A2 , enough non regular dominant weights with the Borel- Weil- Bott property were given.