Quantum Symmetric Pairs and Their Zonal Spherical Functions
Quantum Symmetric Pairs and Their Zonal Spherical Functions
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DOI：
10.1007/s00031-003-0719-9
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发表时间：
2002-04
影响因子：
0.7
通讯作者：
G. Letzter
中科院分区：
文献类型：
--
作者：
G. Letzter
我们研究了最大分裂情况下与量子对称对相关的双不变量和区域球函数的空间。在明显的限制图下，证明了双不变量的空间与与限制根相关的字符群环的Weyl群不变量同构。因此，存在与不可约对称对相关的外尔群不变量子带球函数的唯一集合或（几乎）唯一双参数集合。其中包括用于形成量子对称对的量化包络代数的左共理想子代数的生成器和关系的完整且明确的列表。
We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots. As a consequence, there is either a unique set, or an (almost) unique two-parameter set of Weyl group invariant quantum zonal spherical functions associated to an irreducible symmetric pair. Included is a complete and explicit list of the generators and relations for the left coideal subalgebras of the quantized enveloping algebra used to form quantum symmetric pairs.