刚性表示的一些例子
Some examples of rigid representations
摘要：
考虑Deligne-Simpson问题：{ \em给出了选择共轭类的充分必要条件$C_j\subset GL(n,{\bf C})$（分别为. $c_j\subset gl(n,{\bf C})$）使得存在矩阵$M_j\in C_j$的不可约$(p+1)$ -元组（分别为. $A_j\in c_j$）满足等式$M_1... M_{p+1}=I$（resp. $A_1+... +A_{p+1}=0$）}。矩阵$M_j$和$A_j$被解释为单值算子和黎曼球面上的Fuchsian系统的矩阵剩余。我们给出了矩阵$M_j$的这种$(p+1)$ -元组的存在性的新例子（分别是. $A_j$），它们是{ \em刚性}的，即，一旦类$C_j$（分别为$c_j$）是固定的。对于刚性表示，类$C_j$（分别为$c_j$）等于$2n^2-2$。
英文摘要：
Consider the Deligne-Simpson problem: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ (resp. $c_j\subset gl(n,{\bf C})$) so that there exist irreducible $(p+1)$-tuples of matrices $M_j\in C_j$ (resp. $A_j\in c_j$) satisfying the equality $M_1... M_{p+1}=I$ (resp. $A_1+... +A_{p+1}=0$)}. The matrices $M_j$ and $A_j$ are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann's sphere. We give new examples of existence of such $(p+1)$-tuples of matrices $M_j$ (resp. $A_j$) which are {\em rigid}, i.e. unique up to conjugacy once the classes $C_j$ (resp. $c_j$) are fixed. For rigid representations the sum of the dimensions of the classes $C_j$ (resp. $c_j$) equals $2n^2-2$.
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