On tensor products of positive representations of split real quantum Borel subalgebra Uqq'(bR)
On tensor products of positive representations of split real quantum Borel subalgebra Uqq'(bR)
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分裂实量子Borel子代数Uqq(bR)正表示的张量积
DOI：
10.1090/tran/7110
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Ivan Ip
中科院分区：
文献类型：
--
作者：
Ivan Ip
我们研究了Borel子代数上分裂实量子群的正表示。我们证明了该约束与参数无关。此外，我们还证明了它可以由前面定义的乘子Hopf代数的GNS-表示来构造，这使得我们可以利用“乘法酉性”的理论来分解它们的张量积。具体地说，量子突变算符可以从重数模构造出来，这将是从表象理论的角度构造量子高等Teichmüler理论的重要组成部分，推广了Frenkel-Kim早期的工作。参考文献
We study the positive representationsof split real quantum groupsrestricted to the Borel subalgebra. We prove that the restriction is independent of the parameter. Furthermore, we prove that it can be constructed from the GNS-representation of the multiplier Hopf algebradefined earlier, which allows us to decompose their tensor product using the theory of the “multiplicative unitary”. In particular, the quantum mutation operator can be constructed from the multiplicity module, which will be an essential ingredient in the construction of quantum higher Teichmüller theory from the perspective of representation theory, generalizing earlier work by Frenkel-Kim. References