Q: Is $B(w_1 w_2)B = (Bw_1B)(Bw_2B)$? Let $B$ be a Borel subgroup of $GL_n$ and $W$ the Weyl group of $GL_n$. Let $w_1, w_2 \in W$. Is $B(w_1 w_2)B = (Bw_1B)(Bw_2B)$? If this is true. How to prove it? Thank you very much.
Edit: If $l(w_1 w_2) = l(w_1) + l(w_2)$, is $B(w_1 w_2)B = (Bw_1B)(Bw_2B)$? 
