关于Clifford-Lipschitz群与q-对称群的关系
On the relation of Clifford-Lipschitz groups to q-symmetric groups
摘要：
可以证明，在多向量的Clifford代数中找到Hecke代数的表示是可能的。这些Clifford代数具有唯一的阶化和可能的非对称双线性型。对于非一般的q，由于q ->1的群代数的同构，Hecke代数表示可以通过对称群的Young tableaux来分类。由于旋量可以被构造为通过左（右）作用于本原幂等元而获得的极小左（右）理想的元素，因此我们能够从对应于适当对称类型的q-Young算子构造q-旋量。证明了Clifford双线性型中的反对称部分是必要的。q-变形的反射（Hecke发电机），可以得到甚至多矢量聚合呈现这种对称性的复合之一。在这种构造中，只能使自旋组变形，但不能使销组变形。该方法与投影解释密切相关。
英文摘要：
It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra representations can be classified, for non-generic q, by Young tableaux of the symmetric group due to the isomorphy of the group algebras for q ->1. Since spinors can be constructed as elements of minimal left (right) ideals obtained by the left (right) action on primitive idempotents, we are able to construct q-spinors from q-Young operators corresponding to the appropriate symmetry type. It turns out that an anti-symmetric part in the Clifford bilinear form is necessary. q-deformed reflections (Hecke generators) can be obtained only for even multivector aggregates rendering this symmetry a composite one. In this construction one is able to deform spin groups only, though not pin groups. The method is closely related to a projective interpretation.
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