Title: Shuffle algebras and their integral forms: specialization map approach in types $C_n$ and $D_n$ Show Chinese title

Title: 混洗代数及其积分形式：$C_n$ 和 $D_n$ 类型中的特殊化映射方法

Abstract: We construct a family of PBWD bases for the positive subalgebras of quantum loop algebras of type $C_n$ and $D_n$, as well as their Lusztig and RTT integral forms, in the new Drinfeld realization. We also establish a shuffle algebra realization of these $\mathbb{Q}(v)$-algebras (proved earlier in arXiv:2102.11269 by completely different tools) and generalize the latter to the above $\mathbb{Z}[v,v^{-1}]$-forms. The rational counterparts provide shuffle algebra realizations of positive subalgebras of type $C_n$ and $D_n$ Yangians and their Drinfeld-Gavarini duals. While this naturally generalizes our earlier treatment of the classical type $B_n$ in arXiv:2305.00810 and $A_n$ in arXiv:1808.09536, the specialization maps in the present setup are more compelling. Show Chinese abstract

Abstract: 我们构造了类型$C_n$和$D_n$的量子环代数的正子代数及其 Lusztig 和 RTT 整数形式的 PBWD 基础，在新的 Drinfeld 表示中。 我们还建立了这些$\mathbb{Q}(v)$-代数的乘积代数实现（在 arXiv:2102.11269 中之前用完全不同的工具证明），并将后者推广到上述$\mathbb{Z}[v,v^{-1}]$-形式。 有理对应物提供了类型$C_n$和$D_n$的正子代数的乘积代数实现，以及杨代数及其 Drinfeld-Gavarini 对偶。 虽然这自然推广了我们之前在 arXiv:2305.00810 中对经典类型$B_n$和 arXiv:1808.09536 中的$A_n$的处理，但目前设置中的特化映射更具说服力。