论文标题
$ u_q（\ Mathfrak {gl} _n）$的$ q $ - 苏联表示的影响
Affinization of $q$-oscillator representations of $U_q(\mathfrak{gl}_n)$
论文作者
论文摘要
我们介绍了一个类别$ \ wideHat {\ Mathcal {o}} _ {\ rm OSC} $ $ q $ - oscilltator表示量子仿射代数$ u_q（\ wideHat {\ mathfrak {gl}} _ n）$。我们表明，$ \ wideHat {\ Mathcal {o}} _ {\ rm osc} $具有不可减至的表示的家族，它自然对应于有限的二维不可约束表示，量子不相关的offine offine offine offine offine offine offine offine offine offine offine offine type $ a $ a $。它是通过构建$ q $ scoscillter的类别来完成的，该类别的$ a $ a $ a $的量子仿射超gerge词将这两个不可约的表示家族插入。 The category $\widehat{\mathcal{O}}_{\rm osc}$ can be viewed as a quantum affine analogue of the semisimple tensor category generated by unitarizable highest weight representations of $\mathfrak{gl}_{u+v}$ ($n=u+v$) appearing in the $（\ mathfrak {gl} _ {u+v}，\ mathfrak {gl} _ \ ell）$ - 在玻色孔空间上二重性。
We introduce a category $\widehat{\mathcal{O}}_{\rm osc}$ of $q$-oscillator representations of the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_n)$. We show that $\widehat{\mathcal{O}}_{\rm osc}$ has a family of irreducible representations, which naturally corresponds to finite-dimensional irreducible representations of quantum affine algebra of untwisted affine type $A$. It is done by constructing a category of $q$-oscillator representations of the quantum affine superalgebra of type $A$, which interpolates these two family of irreducible representations. The category $\widehat{\mathcal{O}}_{\rm osc}$ can be viewed as a quantum affine analogue of the semisimple tensor category generated by unitarizable highest weight representations of $\mathfrak{gl}_{u+v}$ ($n=u+v$) appearing in the $(\mathfrak{gl}_{u+v},\mathfrak{gl}_\ell)$-duality on a bosonic Fock space.
