论文标题
项的极端张量产品
Extremal tensor products of Demazure crystals
论文作者
论文摘要
氮杂晶体是最高重量不可约$ \ mathfrak {g} $ - 晶体的子晶体。在本文中，我们研究了称为极端晶体的较大类子晶体的张量产品，并为何时何时何时获得了果酱晶体的张量产物，并给出了局部表征。然后，我们表明，当且仅当张量产物是极端的时，纽唑晶体的张量会分解为项的直接总和，从而为何时征服了氮杂晶体的张力产物本身就是emazure，从而提供了足够且必要的局部标准。作为应用程序，我们表明，任何NAMAZURE CRYSTAL的张量平方中的主要组件总是尚率。
Demazure crystals are subcrystals of highest weight irreducible $\mathfrak{g}$-crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal, and give a local characterization for exactly when the tensor product of Demazure crystals is extremal. We then show that tensor products of Demazure crystals decompose into direct sums of Demazure crystals if and only if the tensor product is extremal, thus providing a sufficient and necessary local criterion for when the tensor product of Demazure crystals is itself Demazure. As an application, we show that the primary component in the tensor square of any Demazure crystal is always Demazure.
