有限阿贝尔群的组合学与Weil表示
Combinatorics of finite abelian groups and Weil representations
摘要：
证明了与奇阶有限阿贝尔群相关的辛群的Weil表示具有无乘法分解.当阿贝尔群是p-准素群时，Weil表示中出现的不可约表示被一个与p无关的偏序集参数化.当p变化时，对应于每个参数的不可约表示的维数被证明是p中的一个多项式. Weil表示的交换代数有一个由另一个独立于p的偏序集索引的基.计算了投影算子在不可约不变子空间上的展开式.这些结果仍然有效，在更一般的设置，在一个戴德金整环上生成的扭模。
英文摘要：
The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil representation are parametrized by a partially ordered set which is independent of p. As p varies, the dimension of the irreducible representation corresponding to each parameter is shown to be a polynomial in p which is calculated explicitly. The commuting algebra of the Weil representation has a basis indexed by another partially ordered set which is independent of p. The expansions of the projection operators onto the irreducible invariant subspaces in terms of this basis are calculated. The coefficients are again polynomials in p. These results remain valid in the more general setting of finitely generated torsion modules over a Dedekind domain.
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