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man111
 Post subject: quadratic-inequality
PostPosted: Sat, 25 Sep 2010 08:02:00 UTC 
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$\ Find all values of a for which all the solution of the in-equation\\ ax^2 -2(a^2-3)x-12a \geq 0\\ $\ are the solution of the in-equation\\ x^2 -49 \geq\ 0.
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outermeasure
 Post subject: Re: quadratic-inequality
PostPosted: Sat, 25 Sep 2010 12:49:53 UTC 
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man111 wrote:
Find all values of a for which all the solution of the in-equation
ax^2 -2(a^2-3)x-12a \geq 0
are the solution of the in-equation
x^2 -49 \geq 0


Again, what inequations? I see no inequations here.

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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