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Revision as of 04:32, 1 May 2009
, 04:32, 1 May 2009→Commentary Note 12.1
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The matrix representation of <math>\mathit{l}^\mathrm{w}\!</math> is very instructive to examine at this point, and even shows the sense behind the name ''involution''.
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>\operatorname{Mat}(\mathit{l}^\mathrm{w}) ~=~ \operatorname{Mat}(\mathit{l})^{\operatorname{Mat}(\mathrm{w})} ~=~ \mathfrak{L}^\mathfrak{W}</math>
| height="60" | <math>\operatorname{Mat}(\mathit{l}^\mathrm{w}) ~=~ \operatorname{Mat}(\mathit{l})^{\operatorname{Mat}(\mathrm{w})} ~=~ \mathfrak{L}^\mathfrak{W}</math>
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| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_{a} ~=~ \prod_{x \in X} \mathfrak{L}_{ax}^{\mathfrak{W}_{x}}</math>
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===Commentary Note 12.2===
===Commentary Note 12.2===
