AI 中文总结
研究例外型量子仿射超代数最小非平凡不可约表示，给出D$_{2\vert 1;\alpha}$、F$_{3\vert 1}$、G$_{2\vert 1}$型在两种实现下的显式公式，借此得到相应$R$ - 矩阵的显式表达式。
AI 中文摘要
我们给出了量子仿射超代数在D$_{2\vert 1;\alpha}$型（$\dim V = 18$，全费米子奇偶性）、F$_{3\vert 1}$型（$\dim V = 41$，特殊奇偶性）和G$_{2\vert 1}$型（$\dim V = 32$，特殊奇偶性）中最小非平凡不可约表示$V$的显式公式，涵盖Drinfeld - Jimbo实现和新Drinfeld实现。利用此信息得到相应$R$ - 矩阵的显式表达式。
英文摘要
We give explicit formulas for the smallest non-trivial irreducible representation $V$ of quantum affine superalgebras in types D$_{2\vert 1;α}$, $\dim V=18$ (in the all-fermionic parity), F$_{3\vert 1}$, $\dim V=41$ (in the distinguished parity), and G$_{2\vert 1}$, $\dim V=32$ (in the distinguished parity), both in the Drinfeld-Jimbo and in the new Drinfeld realizations. We use this information to obtain an explicit expression for the corresponding $R$-matrices.
CommentsLatex, 27 pages, 6 figures
