论文标题
通过网折叠旋转对称的tableaux
Folding rotationally symmetrical tableaux via webs
论文作者
论文摘要
带有2或3行的矩形标准Young Tableaux与$ U_Q（\ Mathfrak {sl} _2）$ - 网络和$ u_q（\ Mathfrak {sl} _3）$ - 网络进行两行。当$ w $是具有反射对称性的网络时，相应的tableau $ t_w $具有旋转对称性。折叠$ T_W $将其转换为Domino Tableau $ D_W $。我们研究这些对应关系之间的关系。对于2行tableaux，折叠旋转对称的图表对应于沿其对称性轴“字面上折叠”网络。对于$ 3 $ -ROW TABLEAUX，我们提供了简单的算法，该算法可在对称网和Domino Tableaux（在两个方向上）之间提供直接的徒图图。这些算法的这些详细信息反映了$ d_w $对应于“ $ W $ modulo对称性”的直观想法。
Rectangular standard Young tableaux with 2 or 3 rows are in bijection with $U_q(\mathfrak{sl}_2)$-webs and $U_q(\mathfrak{sl}_3)$-webs respectively. When $W$ is a web with a reflection symmetry, the corresponding tableau $T_W$ has a rotational symmetry. Folding $T_W$ transforms it into a domino tableau $D_W$. We study the relationships between these correspondences. For 2-row tableaux, folding a rotationally symmetric tableau corresponds to "literally folding" the web along its axis of symmetry. For $3$-row tableaux, we give simple algorithms, which provide direct bijective maps between symmetrical webs and domino tableaux (in both directions). These details of these algorithms reflect the intuitive idea that $D_W$ corresponds to "$W$ modulo symmetry".
