0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析

上篇：0Yψ vs HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析

分析1：(0)(1,1,1,1)~(0)(1,1,1,1)(2,1)

0Yψ	强LPrSS投影	拓展HPrSSψ	弱LPrSS投影	弱LPrSS向上投影	BMS
$\psi ({\mathrm{\Omega }}_3)$	$\psi (a)$	$\psi ({\mathrm{\Omega }}_{\omega })$	$\psi ({\sigma }^{\omega }a)$	$\psi ({\psi }_S(\sigma S\times \omega ))$	(0)(1,1,1,1)
$\psi ({\mathrm{\Omega }}_3+\mathrm{\Omega })$	$\psi (a+\mathrm{\Omega })$	$\psi ({\mathrm{\Omega }}_{\omega }+\mathrm{\Omega })$	$\psi ({\sigma }^{\omega }a+\mathrm{\Omega })$	$\psi ({\psi }_S(\sigma S\times \omega )+\mathrm{\Omega })$	(0)(1,1,1,1)(1,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_3))$	$\psi (a+{\psi }_1({\mathrm{\Omega }}_3))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_3))$	$\psi ({\sigma }^{\omega }a+{\psi }_1({\mathrm{\Omega }}_3))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1({\mathrm{\Omega }}_3))$	(0)(1,1,1,1)(1,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\psi }_3({\mathrm{\Omega }}_5)))$	$\psi (a+{\psi }_1({\mathrm{\Omega }}_4))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\psi }_3({\mathrm{\Omega }}_5)))$	$\psi ({\sigma }^{\omega }a+{\psi }_1({\mathrm{\Omega }}_4))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1({\mathrm{\Omega }}_4))$	(0)(1,1,1,1)(1,1)(2,2,1)(3,3,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\psi }_3({\mathrm{\Omega }}_6)))$	$\psi (a+{\psi }_1({\psi }_a(a_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_4))$	$\psi ({\sigma }^{\omega }a+{\psi }_1(a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1(a))$	(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\psi }_3({\psi }_6({\mathrm{\Omega }}_{10}))))$	$\psi (a+{\psi }_1({\psi }_a({\psi }_{\sigma a}(\sigma a_2))))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_5))$	$\psi ({\sigma }^{\omega }a+{\psi }_1(\sigma a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1({\psi }_S(\sigma S\times 3)))$	(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)(4,4,3)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_4))$	$\psi (a+{\psi }_1(a))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }))$	$\psi ({\sigma }^{\omega }a+{\psi }_1({\sigma }^{\omega }a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1({\psi }_S(\sigma S\times \omega )))$	(0)(1,1,1,1)(1,1)(2,2,1,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_4+{\mathrm{\Omega }}_2))$	$\psi (a+{\psi }_1(a+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2))$	$\psi ({\sigma }^{\omega }a+{\psi }_1({\sigma }^{\omega }a+{\mathrm{\Omega }}_2))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1({\psi }_S(\sigma S\times \omega )+{\mathrm{\Omega }}_2))$	(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_4+{\psi }_2({\mathrm{\Omega }}_5)))$	$\psi (a+{\psi }_1(a+{\psi }_2(a)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_{\omega })))$	$\psi ({\sigma }^{\omega }a+{\psi }_1({\sigma }^{\omega }a+{\psi }_2({\sigma }^{\omega }a)))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_1({\psi }_S(\sigma S\times \omega )+{\psi }_2({\psi }_S(\sigma S\times \omega ))))$	(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)(3,3,1,1)
$\psi ({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_2)$	$\psi (a+{\mathrm{\Omega }}_2)$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2)$	$\psi ({\sigma }^{\omega }a+{\mathrm{\Omega }}_2)$	$\psi ({\psi }_S(\sigma S\times \omega )+{\mathrm{\Omega }}_2)$	(0)(1,1,1,1)(1,1,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4))$	$\psi (a+{\mathrm{\Omega }}_3)$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_4))$	$\psi ({\sigma }^{\omega }a+{\mathrm{\Omega }}_3)$	$\psi ({\psi }_S(\sigma S\times \omega )+{\mathrm{\Omega }}_3)$	(0)(1,1,1,1)(1,1,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4\omega ))$	$\psi (a+{\mathrm{\Omega }}_{\omega })$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_4\omega ))$	$\psi ({\sigma }^{\omega }a+{\mathrm{\Omega }}_{\omega })$	$\psi ({\psi }_S(\sigma S\times \omega )+{\mathrm{\Omega }}_{\omega })$	(0)(1,1,1,1)(1,1,1)(2,2,1)(3)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_3))$	$\psi (a+{\psi }_a({\mathrm{\Omega }}_{a+1}a))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_3))$	$\psi ({\sigma }^{\omega }a+{\psi }_a({\mathrm{\Omega }}_{a+1}a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a({\mathrm{\Omega }}_{a+1}a))$	(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4^2))$	$\psi (a+{\psi }_a({\mathrm{\Omega }}_{a+1}^2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_4^2))$	$\psi ({\sigma }^{\omega }a+{\psi }_a({\mathrm{\Omega }}_{a+1}^2))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a({\mathrm{\Omega }}_{a+1}^2))$	(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\psi }_4({\mathrm{\Omega }}_5)))$	$\psi (a+{\psi }_a({\epsilon }_{{\mathrm{\Omega }}_{a+1}+1}))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\psi }_4({\mathrm{\Omega }}_5)))$	$\psi ({\sigma }^{\omega }a+{\psi }_a({\epsilon }_{{\mathrm{\Omega }}_{a+1}+1}))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a({\epsilon }_{{\mathrm{\Omega }}_{a+1}+1}))$	(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\psi }_4({\mathrm{\Omega }}_6)))$	$\psi (a+{\psi }_a({\mathrm{\Omega }}_{a+2}))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\psi }_4({\mathrm{\Omega }}_6)))$	$\psi ({\sigma }^{\omega }a+{\psi }_a({\mathrm{\Omega }}_{a+2}))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a({\mathrm{\Omega }}_{a+2}))$	(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_5))$	$\psi (a+{\psi }_a(a_2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_5))$	$\psi ({\sigma }^{\omega }a+{\psi }_a(a_2))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a(a_2))$	(0)(1,1,1,1)(1,1,1)(2,2,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\psi }_5({\mathrm{\Omega }}_8)))$	$\psi (a+{\psi }_a(a_3))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\psi }_5({\mathrm{\Omega }}_8)))$	$\psi ({\sigma }^{\omega }a+{\psi }_a(a_3))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a(a_3))$	(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\psi }_5({\mathrm{\Omega }}_9)))$	$\psi (a+{\psi }_a({\psi }_{\sigma a}(\sigma a_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_6))$	$\psi ({\sigma }^{\omega }a+{\psi }_a(\sigma a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a({\psi }_S(\sigma S\times 3)))$	(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,3)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6))$	$\psi (a+{\psi }_a(\sigma a))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_{\omega }))$	$\psi ({\sigma }^{\omega }a+{\psi }_a({\sigma }^{\omega }a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_a({\psi }_S(\sigma S\times \omega )))$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6+{\mathrm{\Omega }}_5))$	$\psi (a+{\psi }_a(\sigma a+a_2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_3)$	$\psi ({\sigma }^{\omega }a+a)$	$\psi ({\psi }_S(\sigma S\times \omega )+a)$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6+{\psi }_5({\mathrm{\Omega }}_8)))$	$\psi (a+{\psi }_a(\sigma a+a_3))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_3({\mathrm{\Omega }}_6))$	$\psi ({\sigma }^{\omega }a+a_2)$	$\psi ({\psi }_S(\sigma S\times \omega )+a_2)$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,2)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6+{\psi }_5({\mathrm{\Omega }}_9)))$	$\psi (a+{\psi }_a(\sigma a+{\psi }_{\sigma a}(\sigma a_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_3({\mathrm{\Omega }}_7))$	$\psi ({\sigma }^{\omega }a+{\psi }_{\sigma a}(\sigma a_2))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_S(\sigma S\times 2+S_2))$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6+{\psi }_5({\mathrm{\Omega }}_{10})))$	$\psi (a+{\psi }_a(\sigma a+{\psi }_{\sigma a}({\sigma }^{2}a)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_3({\mathrm{\Omega }}_{\omega }))$	$\psi ({\sigma }^{\omega }a+{\psi }_{\sigma a}({\sigma }^{\omega }a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_{{\psi }_S(\sigma S\times 3)}({\psi }_S(\sigma S\times \omega )))$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6+{\psi }_5({\mathrm{\Omega }}_{10}+{\mathrm{\Omega }}_9)))$	$\psi (a+{\psi }_a(\sigma a+{\psi }_{\sigma a}({\sigma }^{2}a+\sigma a_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_4)$	$\psi ({\sigma }^{\omega }a+\sigma a)$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_S(\sigma S\times 3))$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)
$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_6+{\psi }_5({\mathrm{\Omega }}_{10}+{\psi }_9({\mathrm{\Omega }}_{15}))))$	$\psi (a+{\psi }_a(\sigma a+{\psi }_{\sigma a}({\sigma }^{2}a+{\psi }_{{\sigma }^{2}a}({\sigma }^{3}a))))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_4({\mathrm{\Omega }}_{\omega }))$	$\psi ({\sigma }^{\omega }a+{\psi }_{{\sigma }^{2}a}({\sigma }^{\omega }a))$	$\psi ({\psi }_S(\sigma S\times \omega )+{\psi }_{{\psi }_S(\sigma S\times 4)}({\psi }_S(\sigma S\times \omega )))$	(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)(4,4,4,1)
$\psi ({\mathrm{\Omega }}_{3}2)$	$\psi (a2)$	$\psi ({\mathrm{\Omega }}_{\omega }2)$	$\psi ({\sigma }^{\omega }a2)$	$\psi ({\psi }_S(\sigma S\times \omega )\times 2)$	(0)(1,1,1,1)(1,1,1,1)
$\psi ({\mathrm{\Omega }}_{3}2+{\mathrm{\Omega }}_2)$	$\psi (a2+{\mathrm{\Omega }}_2)$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\mathrm{\Omega }}_2)$	$\psi ({\sigma }^{\omega }a2+{\mathrm{\Omega }}_2)$	$\psi ({\psi }_S(\sigma S\times \omega )\times 2+{\mathrm{\Omega }}_2)$	(0)(1,1,1,1)(1,1,1,1)(1,1,1)
$\psi ({\mathrm{\Omega }}_{3}2+{\psi }_2({\mathrm{\Omega }}_6))$	$\psi (a2+{\psi }_a(\sigma a))$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\psi }_2({\mathrm{\Omega }}_{\omega }))$	$\psi ({\sigma }^{\omega }a2+{\psi }_a({\sigma }^{\omega }a))$	$\psi ({\psi }_S(\sigma S\times \omega )\times 2+{\psi }_a({\psi }_S(\sigma S\times \omega )))$	(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)
$\psi ({\mathrm{\Omega }}_{3}2+{\psi }_2({\mathrm{\Omega }}_{6}2))$	$\psi (a2+{\psi }_a(\sigma a2))$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\psi }_2({\mathrm{\Omega }}_{\omega }2))$	$\psi ({\sigma }^{\omega }a2+{\psi }_a({\sigma }^{\omega }a2))$	$\psi ({\psi }_S(\sigma S\times \omega )\times 2+{\psi }_a({\psi }_S(\sigma S\times \omega )\times 2))$	(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)
$\psi ({\mathrm{\Omega }}_{3}2+{\psi }_2({\mathrm{\Omega }}_{6}2+{\mathrm{\Omega }}_5))$	$\psi (a2+{\psi }_a(\sigma a2+a_2))$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\mathrm{\Omega }}_3)$	$\psi ({\sigma }^{\omega }a2+a)$	$\psi ({\psi }_S(\sigma S\times \omega )\times 2+a)$	(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)(2,2,2)
$\psi ({\mathrm{\Omega }}_{3}3)$	$\psi (a3)$	$\psi ({\mathrm{\Omega }}_{\omega }3)$	$\psi ({\sigma }^{\omega }a3)$	$\psi ({\psi }_S(\sigma S\times \omega )\times 3)$	(0)(1,1,1,1)(1,1,1,1)(1,1,1,1)
$\psi ({\mathrm{\Omega }}_3\omega )$	$\psi (a\omega )$	$\psi ({\mathrm{\Omega }}_{\omega }\omega )$	$\psi ({\sigma }^{\omega }a\omega )$	$\psi ({\psi }_S(\sigma S\times \omega )\times \omega )$	(0)(1,1,1,1)(2)
$\psi ({\mathrm{\Omega }}_3\times (\omega +1))$	$\psi (a\times (\omega +1))$	$\psi ({\mathrm{\Omega }}_{\omega }\times (\omega +1))$	$\psi ({\sigma }^{\omega }a\times (\omega +1))$	$\psi ({\psi }_S(\sigma S\times \omega )\times (\omega +1))$	(0)(1,1,1,1)(2)(1,1,1,1)
$\psi ({\mathrm{\Omega }}_3\times \omega 2)$	$\psi (a\times \omega 2)$	$\psi ({\mathrm{\Omega }}_{\omega }\times \omega 2)$	$\psi ({\sigma }^{\omega }a\times \omega 2)$	$\psi ({\psi }_S(\sigma S\times \omega )\times \omega 2)$	(0)(1,1,1,1)(2)(1,1,1,1)(2)
$\psi ({\mathrm{\Omega }}_3\times {\omega }^2)$	$\psi (a\times {\omega }^2)$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\omega }^2)$	$\psi ({\sigma }^{\omega }a\times {\omega }^2)$	$\psi ({\psi }_S(\sigma S\times \omega )\times {\omega }^2)$	(0)(1,1,1,1)(2)(2)
$\psi ({\mathrm{\Omega }}_3\times {\omega }^{\omega })$	$\psi (a\times {\omega }^{\omega })$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\omega }^{\omega })$	$\psi ({\sigma }^{\omega }a\times {\omega }^{\omega })$	$\psi ({\psi }_S(\sigma S\times \omega )\times {\omega }^{\omega })$	(0)(1,1,1,1)(2)(3)
$\psi ({\mathrm{\Omega }}_3\times {\epsilon }_0)$	$\psi (a\times {\epsilon }_0)$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\epsilon }_0)$	$\psi ({\sigma }^{\omega }a\times {\epsilon }_0)$	$\psi ({\psi }_S(\sigma S\times \omega )\times {\epsilon }_0)$	(0)(1,1,1,1)(2)(3,1)
$\psi ({\mathrm{\Omega }}_3\times \psi ({\mathrm{\Omega }}_2))$	$\psi (a\times \psi ({\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }\times \psi ({\mathrm{\Omega }}_2))$	$\psi ({\sigma }^{\omega }a\times \psi ({\mathrm{\Omega }}_2))$	$\psi ({\psi }_S(\sigma S\times \omega )\times \psi ({\mathrm{\Omega }}_2))$	(0)(1,1,1,1)(2)(3,1,1)
$\psi ({\mathrm{\Omega }}_3\times \psi ({\mathrm{\Omega }}_3))$	$\psi (a\times \psi (a))$	$\psi ({\mathrm{\Omega }}_{\omega }\times \psi ({\mathrm{\Omega }}_{\omega }))$	$\psi ({\sigma }^{\omega }a\times \psi ({\sigma }^{\omega }a))$	$\psi ({\psi }_S(\sigma S\times \omega )\times \psi ({\psi }_S(\sigma S\times \omega )))$	(0)(1,1,1,1)(2)(3,1,1,1)
$\psi ({\mathrm{\Omega }}_3\mathrm{\Omega })$	$\psi (a\mathrm{\Omega })$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega })$	$\psi ({\sigma }^{\omega }a\mathrm{\Omega })$	$\psi ({\psi }_S(\sigma S\times \omega )\times \mathrm{\Omega })$	(0)(1,1,1,1)(2,1)