Orthogonal Polynomials of Compact Simple Lie Groups

Table 2

The irreducible 𝐶- and 𝑆-polynomials of 𝐴₂ of degree up to 4. From any polynomial 𝐶_(𝑎,𝑏) or 𝑆_(𝑎,𝑏) we obtain 𝐶_(𝑏,𝑎) or 𝑆_(𝑏,𝑎), respectively, by interchanging 𝑋₁ and 𝑋₂.

𝐶 polynomials		𝑆 polynomials
#=0		#=0
𝐶(1,1)	𝑋1𝑋2−3	𝑆(1,1)	𝑋1𝑋2−1
𝐶(3,0)	𝑋^31−3𝑋1𝑋2+3	𝑆(0,3)	𝑋^32−2𝑋1𝑋2+1
𝐶(2,2)	𝑋^21𝑋^22−2𝑋^31−2𝑋^32+4𝑋1𝑋2−3	𝑆(2,2)	𝑋^21𝑋^22−𝑋^31−𝑋^32
#=1		#=1
𝐶(1,0)	𝑋1	𝑆(1,0)	𝑋1
𝐶(0,2)	𝑋^22−2𝑋1	𝑆(0,2)	𝑋^22−𝑋1
𝐶(2,1)	𝑋^21𝑋2−2𝑋^22−𝑋1	𝑆(2,1)	𝑋^21𝑋2−𝑋^22−𝑋1
𝐶(1,3)	𝑋1𝑋^32−3𝑋^21𝑋2−𝑋^22+5𝑋1	𝑆(1,3)	𝑋1𝑋^32−2𝑋^21𝑋2−𝑋^22+2𝑋2
𝐶(4,0)	𝑋^41−4𝑋^21𝑋2+2𝑋^22+4𝑋1	𝑆(4,0)	𝑋^41−3𝑋^21𝑋2+𝑋^22+𝑋1+𝑋2