D型Fock空间与量子对称对  

Type D Fock Spaces and Quantum Symmetric Pairs

作　　者：EHRIG Michael 甘凯轩 EHRIG Michael;GAN Kaixuan(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 102488,China)

机构地区：[1]北京理工大学数学与统计学院,北京102488

出　　处：《北京理工大学学报》2023年第8期878-884,共7页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(12050410261)。

摘　　要：Misra和Miwa通过Fock空间构造了量子仿射代数Uv(sle)的自然表示.这将Uq(slN)的Weyl模与Uv(sle)在Fock空间上的作用联系起来,其中q是单位根.对于D型量子群Uq(so2N),通过推广A型Fock空间上的仿射量子群作用,构造了一个从有限维Uq(so2N)模的Grothendieck群到广义Fock空间的嵌入,并且定义了仿射量子对称对在这些空间上的作用.由此将仿射量子对称对的作用与单位根处的量子群的邻接原理和张量积分解联系起来,其中Uq(so2N)有限维模范畴中的张量积分解与A型量子群Uq(slN)的有限维模范畴中的张量积分解类似.A celebrated construction of the natural representation of the quantized affine algebra Uv(sLe)is the:Fock space by Misra and Miwa.This relates the classes of Weyl modules for Ug(slv)where q is a root of unity to the action of Uv(sle)on the Fock space.For quantum group Ug(sD2v)of type D,an embedding of the Grothen-dieck group of finite dimensional Uq(s02v)-modules into generalized Fock spaces was constructed and an action of an affine quantum symmetric pair on these spaces was defined.This relates the action of the affine quantum symmetric pair to the linkage principal for quantum groups at a root of unity and tensor product multiplicities in analogy to that for finite dimensional module categories of the quantum group Ug(slv).

关 键 词：FOCK空间 量子对称对 单位根处的量子群 

分 类 号：O152.5[理学—数学]