一类量子自同态代数的胞腔性
Cellularity of certain quantum endomorphism algebras
摘要：
我们展示了所有的正整数r，一个明确的细胞结构的自同态代数的r '次张量幂的积分形式的Weyl模块的量化包络代数的最高权d的SL 2。当q被特化为大于d阶的单位单位根时，我们考虑张量幂幂的相应特化。我们证明了一个一般性的结果，它给出了充分条件的交换性专门化与自同态代数，另一个涉及的多重性不可分解的和的维数的简单模块的自同态代数。我们的细胞性结果，然后让我们证明，知识的维度的简单模块的专门细胞代数以上是等价的知识的重量多重性的倾斜模块的专门量子群。在最后一节中，我们独立地确定了量子s1 ~ 2的不可分解倾斜模的权重数和自同态代数的分解数。我们指出这些数字中的任何一组如何决定另一组。
英文摘要：
We exhibit for all positive integers r, an explicit cellular structure for the endomorphism algebra of the r'th tensor power of an integral form of the Weyl module with highest weight d of the quantised enveloping algebra of sl2. When q is specialised to a root of unity of order bigger than d, we consider the corresponding specialisation of the tensor power. We prove one general result which gives sufficient conditions for the commutativity of specialisation with the taking of endomorphism algebras, and another which relates the multiplicities of indecomposable summands to the dimensions of simple modules for an endomorphism algebra. Our cellularity result then allows us to prove that knowledge of the dimensions of the simple modules of the specialised cellular algebra above is equivalent to knowledge of the weight multiplicities of the tilting modules for the specialised quantum group. In the final section we independently determine the weight multiplicities of indecomposable tilting modules for quantum sl2, and the decomposition numbers of the endomorphism algebras. We indicate how either one of these sets of numbers determines the other.
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