Square-integrable factor representations of locally compact groups
Square-integrable factor representations of locally compact groups
复制标题
局部紧群的平方可积因子表示
DOI：
--
复制
发表时间：
1978
期刊：
影响因子：
--
通讯作者：
Jonathan Rosenberg
中科院分区：
文献类型：
--
作者：
Jonathan Rosenberg
.将著名的平方可积表示理论推广到准素表示（不一定是I型）拟包含在正则表示或由局部紧群（不一定是幺模）的中心特征标导出的表示中的情形，得到了它与群C*-代数的本原理想空间拓扑的关系.离散和几乎连通群的情况下进行了更详细的研究，它表明，对于这样的群体，平方可积因子表示必须是可追踪的。对于连通李群，这些表示可以（原则上）使用L的复杂构造确定到准等价。对于I型单连通可解李群，其特征化约为C. C.摩尔和沃尔夫。在幺模指数群的情况下，基本上一切都和幂零的情况一样（包括L2（G/T）分解中重数的结果，T是G的离散一致子群）。最后，证明了与I型可解李群相同的准则刻画了R.豪
. The well-known theory of square-integrable representations is generalized to the case of primary representations (not necessarily type I) quasi-contained in either the regular representation or the representation induced from a character of the center of a (not necessarily unimodular) locally compact group, and relations with the topology of the primitive ideal space of the group C*-algebra are obtained. The cases of discrete and almost connected groups are examined in more detail, and it is shown that for such groups, square-integrable factor representations must be traceable. For connected Lie groups, these representations can (in principle) be determined up to quasi-equivalence using a complicated construction of L. Pukanszky-for type I simply connected solvable Lie groups, the characterization reduces to that conjectured by C. C. Moore and J. Wolf. In the case of unimodular exponential groups, essentially everything is as in the nilpotent case (including a result on multiplicities in the decomposition of L2(G/T), T a discrete uniform subgroup of G). Finally, it is shown that the same criterion as for type I solvable Lie groups characterizes the square-integrable representations of certain solvable p-adic groups studied by R. Howe.