超特殊紧群的正则irreducible characters与有限域上的Weil表示
Regular irreducible characters of a hyperspecial compact group and Weil representations over finite fields
摘要：
给出了p为奇数的p进域上约化群的超特殊紧子群的不可约酉表示的一种构造方法。我们的方法是基于Cliffods理论和有限域上的Weil表示。它的工作原理的假设下，平凡的某些舒尔乘子定义的代数群在有限域。平凡性假设在一般线性群的情况下有很好的证据，而在一般正则情况下是很可能的。我们将给出几个典型群的例子，其中舒尔乘子实际上是平凡的。
英文摘要：
A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite fields. It works under an assumption of the triviality of certain Schur multipliers defined for an algebraic group over a finite field. The assumption of the triviality has good evidences in the case of general linear groups and highly probable in regular cases in general. We will give several examples of classical groups where the Schur multipliers are actually trivial.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
