论文标题
稳定范围内的字符对应关系
The character correspondence in the stable range over a p-adic field
论文作者
论文摘要
鉴于一个真实的二对，有一个积分内核运算符，它映射了该组的不可还原可允许表示的分布特征，其较小或相等等级的分布与较大或相等等级的组的不变性。如果对在稳定范围内，并且表示表示为单位，则结果分布是通过Howe的对应关系获得的表示的特征。该结构被转移到P-ADIC案例中，并提出了猜想。 在本说明中，我们在P-ADIC字段上验证了稳定范围内的双对的较弱版本。
Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank. If the pair is in the stable range and if the representation is unitary, then the resulting distribution is the character of the representation obtained via Howe's correspondence. This construction was transferred to the p-adic case and a conjecture was formulated. In this note we verify a weaker version of this conjecture for dual pairs in the stable range over a p-adic field.
