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Let $W$ be the Weyl group corresponding to the maximal torus of the$diag(t_1, . . . , t_{n}, t^{−1}_n, . . . , t^{−1}_1)$ in a Borel group of upper triangular matrices of $\operatorname{SO}_{2n}(\mathbb C)$.

What are the matrices corresponding to simple reflections of $W$?

Let $W$ be the Weyl group corresponding to the maximal torus of the Borel group of upper triangular matrices of $\operatorname{SO}_{2n}(\mathbb C)$.

What are the matrices corresponding to simple reflections of $W$?

Let $W$ be the Weyl group corresponding to the maximal torus $diag(t_1, . . . , t_{n}, t^{−1}_n, . . . , t^{−1}_1)$ in a Borel group of $\operatorname{SO}_{2n}(\mathbb C)$.

What are the matrices corresponding to simple reflections of $W$?

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Ami
Ami
  • 332
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The simple reflections of the Weyl group in $\operatorname{SO}_{2n}(\mathbb C)$

Let $W$ be the Weyl group corresponding to the maximal torus of the Borel group of upper triangular matrices of $\operatorname{SO}_{2n}(\mathbb C)$.

What are the matrices corresponding to simple reflections of $W$?