Orthogonal Polynomials of Compact Simple Lie Groups

Table 7

The irreducible 𝐶 polynomials and 𝑆 polynomials of 𝐴₃.

𝐶 polynomials		𝑆 polynomials
#=0		#=0
𝐶(1,0,1)	−4+𝑋1𝑋3	𝑆(1,0,1)	−1+𝑋1𝑋3
𝐶(0,2,0)	2−2𝑋1𝑋3+𝑋^22	𝑆(0,2,0)	𝑋^22−𝑋1𝑋3
𝐶(0,1,2)	4−𝑋1𝑋3−2𝑋^22+𝑋2𝑋^23	𝑆(0,1,2)	1−𝑋^22−𝑋1𝑋3+𝑋2𝑋^23
𝐶(2,1,0)	4−𝑋1𝑋3+𝑋^21𝑋2−2𝑋^22	𝑆(2,1,0)	1+𝑋^21𝑋2−𝑋^22−𝑋1𝑋3
#=1		#=1
𝐶(1,0,0)	𝑋1	𝑆(1,0,0)	𝑋1
𝐶(0,1,1)	−3𝑋1+𝑋2𝑋3	𝑆(0,1,1)	−𝑋1+𝑋2𝑋3
𝐶(0,0,3)	3𝑋1−3𝑋2𝑋3+𝑋^33	𝑆(0,0,3)	𝑋1−2𝑋2𝑋3+𝑋^33
𝐶(2,0,1)	−𝑋1−2𝑋2𝑋3+𝑋^21𝑋3	𝑆(2,0,1)	−𝑋1+𝑋^21𝑋3−𝑋2𝑋3
𝐶(1,2,0)	5𝑋1−𝑋2𝑋3−2𝑋^21𝑋3+𝑋1𝑋^22	𝑆(1,2,0)	𝑋1+𝑋1𝑋^22−𝑋^21𝑋3−𝑋2𝑋3
#=2		#=2
𝐶(0,1,0)	𝑋2	𝑆(0,1,0)	𝑋2
𝐶(0,0,2)	−2𝑋2+𝑋^23	𝑆(0,0,2)	−𝑋2+𝑋^23
𝐶(2,0,0)	−2𝑋2+𝑋^21	𝑆(2,0,0)	𝑋^21−𝑋2
𝐶(1,1,1)	4𝑋2−3𝑋^23−3𝑋^21+𝑋1𝑋2𝑋3	𝑆(1,1,1)	−𝑋^21−𝑋^23+𝑋1𝑋2𝑋3
#=3		#=3
𝐶(0,0,1)	𝑋3	𝑆(0,0,1)	𝑋3
𝐶(1,1,0)	−3𝑋3+𝑋1𝑋2	𝑆(1,1,0)	𝑋1𝑋2−𝑋3
𝐶(3,0,0)	3𝑋3−3𝑋1𝑋2+𝑋^31	𝑆(3,0,0)	𝑋^31−2𝑋1𝑋2+𝑋3
𝐶(1,0,2)	−𝑋3−2𝑋1𝑋2+𝑋1𝑋^23	𝑆(1,0,2)	−𝑋1𝑋2−𝑋3+𝑋1𝑋^23
𝐶(0,2,1)	5𝑋3−𝑋1𝑋2−2𝑋1𝑋^23+𝑋^22𝑋3	𝑆(0,2,1)	−𝑋1𝑋2−𝑋3−𝑋1𝑋^23+𝑋^22𝑋3