【摘要】 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.更多还原

【Abstract】 This paper introduced a new concept—dominant weight with the Borel-Weil-Bott property on the minimal parabolie subalgebras.It was proved that if λ has the Borel-Weil-Bott property on the minimal parabolie subalgebras,then λ satisfies the Borel-Weil-Bott theory on Uq and that for such λ there is the Uq module isomorphism H0q(λ)■H0q(-w0λ)*,where H0q(λ) is a irreducible Uq module with the highest weight λ.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.更多还原