Exercise 5.4.33

Answers

Let

w = w_{1} + w_{2} + \dots + w_{k}

for some $w_{i} \in W_{i}$ . Thus we have $T (w_{i}) \in W_{i}$ since $W_{i}$ is $T$ -invariant. So we also have

T (w) = T (w_{1}) + T (w_{2}) + \dots + T (w_{k}) \in W_{1} + W_{2} + \dots W_{k} .

jephianlin

2011-06-27 00:00