Orthogonal Polynomials of Compact Simple Lie Groups

Table 4

The irreducible 𝑆 polynomials of 𝐶₂ of degree up to 4.

𝑆 polynomials
#=0
𝑆(0,1)	1+𝑋2
𝑆(2,0)	−2+𝑋^21−𝑋2
𝑆(0,2)	2−𝑋^21+3𝑋2+𝑋^22
𝑆(2,1)	−1−3𝑋2+𝑋^21𝑋2−𝑋^22
𝑆(0,3)	2−𝑋^21+7𝑋2−2𝑋^21𝑋2+5𝑋^22+𝑋^32
𝑆(4,0)	3−4𝑋^21+𝑋^41+4𝑋2−3𝑋^21𝑋2+𝑋^22
𝑆(2,2)	−3+4𝑋^21−𝑋^41−7𝑋2+3𝑋^21𝑋2−5𝑋^22+𝑋^21𝑋^22−𝑋^32
#=1
𝑆(1,0)	𝑋1
𝑆(1,1)	𝑋1𝑋2
𝑆(3,0)	−3𝑋1+𝑋^31−2𝑋1𝑋2
𝑆(1,2)	2𝑋1−𝑋^31+2𝑋1𝑋2+𝑋1𝑋^22
𝑆(3,1)	−4𝑋1𝑋2+𝑋^31𝑋2−2𝑋1𝑋^22
𝑆(1,3)	5𝑋1𝑋2−2𝑋^31𝑋2+4𝑋1𝑋^22+𝑋1𝑋^32