极小抛物子代数上具Borel—Weil—Bott性质的权

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Hq^0（λ）≈Hq^0（-w0λ）＊，且Hq^0（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．

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

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.