We establish an intriguing correspondence between ...

    D4                

                      D             X           P(H) = P       X      H        X         

X ∩ H ⊂ X         D                            !                               X    "      2 × 2 × 2 × 2   #      SLOCC                     D   4

15

4

4



         !   "  #  !  $%%&% #  '( )



*"  +     !       , +   

,    

- .

/0 1  , !  #2 3 43%& ! -

'( )



 5        )6 '7 8 1  ,6   89%:: # ;  )

$



  

%                    

                              &      ' (                                #            ) * +       "#, '                               , '         -           SU(2)           #            !        , '

       A − D − E     .            -   %     SU(2)       A sl (C)    x +x +···+x = 0 D so (C)       x +x x +x +···+x = 0 E e     x +x +x +···+x = 0 e     x x + x + x + · · · + x = 0 E E e     x +x +x +···+x = 0 *               ADE                      /                          SU(2)     !0    *       1  '                 

  2       3       -   /      ADE     4          *      

  -            0   5     0          X        -   G    6   -   P(g)                 X                  g 7  



 



 



n

n+1

n

2n

2 2

n+1 1

n−1 1

6

6

4 1

7

7

3 1 2

8

8

5 1

2 k

2 1 2

3 2

2 3

2 3

3 2

3 2

2 k

2 k

2 3

2 3

2 k

2 k

-'  ADE       #  85                    5 .            , '   D      '         -   so(8) 2      D 3 /    )             SO(4) × SO(4) ⊂ SO(8)   M (C) "     ,'

           24' 9:  4 3               so(8)   %-;""            SO(8)  5                           

∇f

)# 

k

1

k

,    μ       (f, 0)      

        (f, 0)            Ok  I∇f 

μ = C (Ok I∇f ) .

     0      f           ! 

    -            ) * +       )# 

-   [(f, 0)]            %  

   (f, 0)     Sk   #       " +

* &               f ∼ x21 + · · ·+

x2k        f  Sk    f + εh  h ∈ Sk      '   

 !     f ∼ f + εh                     "    #  &&(     [(f, 0)]                     f       # 

        

5        * +                 μ < +∞  ∂ f  ' ∂x ∂x (0) ≤ 2 

2

i

j

D





  ' = 2                

  6   ' = 2              μ < 9       * +            .   2 53 ∂2f (0) ∂xi ∂xj

 An Dn E6 E7 E8   xn+1 xn−1 + xy2 x3 + y4 x3 + xy3 x3 + y5

   n n 6 7 8         " +

, 

      &          

                              

     * +                  # 

   (f, 0)     

  μ  μ = ∞         )   * &    r =   !(' (f, 0)) .  r ≥ 3         .  r = 1        Aμ  .  r = 2 

                            Dμ 

                 μ < 9         Eμ 

          

5   #                    

    E



!#

 !" # $ / " (#