258 
The general formula for this correspondence is : 
Bent eK) LB Thea eS 
from which follows for un, : 
Uni = xin? a ee ee es aes (24) 
From the tables given by Frosenius for the group characters we 
thus find directly the equations expressing the / in the K eg. 
for pb: 
Ki k Kz Ka Koe Rp Rr WENS Ko Ko Ku 
ane a 1 1 i 1 1 1 ea 
ed es ees 1 he 1 ui 
EEE Deh ALT gee Ze ug Ig) MAB Zh OG 
SE OS. PIS. AB GD eee eg eee 
ERE ABS AR in BE ia An 
feos, «RS bag 215 Sa sho whl pa eon leek Beeman 
Brin Pati NOT alach MRT dace Basie aa Mey er oA 
Spar lar 9 _217 0 0 0 9 gen Lord 
100 20. 20" 30. toe 10 A 0 0 9. eta 
She Ho. “20 20-20, STO Oe, LO os Dien eo eta 
Tae Ce 0 eeN O20 OO Oe iCeee 
*) The indices on the left of the operators / will be explained furtheron. 
Thus we have found an expansion that is singly determined for 
every affinor. In fact even for a special affinor no linear relation 
can exist between the operators / without each coefficient separately 
being equal to zero, as is seen immediately by application of one 
of the operators /. This expansion is called the expansion in 
elementary affinors. Using tables as (10) and (25) we might now 
m a 
express the / in A, M, A or M and obtain thusa singly determined 
expansion with respect to alternations or mixings. The following 
way however is more simple and more instructive. 
The elementary operators as the products of two general operators. 
When M,;, + gh, Mix are conjugate to A: Ei i wea then wale Pee 
are annihilated by Mj; therefore they cannot contain y, 21 of the 
principal units 7. In the same way 4,,..., Ar are annihilated by 
M,, and M;,, so that they cannot contain y,>1 further principal 
(25) 
