Some exact formulas on quaternion unitary groups
Some exact formulas on quaternion unitary groups
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四元数酉群的一些精确公式
DOI：
10.1515/crll.1999.509.67
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
G. Shimura
中科院分区：
文献类型：
--
作者：
G. Shimura
本文的目的是在辛情形中发展一个理论，在一定程度上，与我们在[S5]和[S6]中在酉和正交情形中所做的理论平行。由于我们主要对非分裂情形感兴趣，我们的群可以被给出为中心为代数数域F的除四元数代数B上的四元数厄米特形式φ的酉群Gφ。更精确地说，我们取一个秩为n的自由左B-模V，和一个B-值埃尔米特形式$使得$和$对于$和$，其中$是B的主对合。则Gφ由V的所有B-线性自同构α组成，使得φ（xα，yα）= φ（x，y）。
The purpose of the present paper is to develop a theory in the symplectic case parallel, to a certain extent, to those we did in the unitary and orthogonal cases in [S5] and [S6]. Since we are mainly interested in the nonsplit case, our group can be given as the unitary group Gφ of a quaternion hermitian form φ over a division quaternion algebra B whose center is an algebraic number field F. To be precise, we take a free left B-module V of rank n, and a B-valued hermitian form $ such that $ and $ for $ and $, where $ is the main involution of B. Then Gφ consists of all the B-linear automorphisms α of V such that φ(xα, yα) = φ(x, y).