Orthogonal Polynomials of Compact Simple Lie Groups

Table 6

The irreducible 𝑆_(𝑎,𝑏) polynomials of 𝐺₂ with 𝑎+𝑏⩽5.

𝑆 polynomials
𝑆(0,1)	𝑋2+1
𝑆(1,0)	𝑋1+𝑋2+2
𝑆(0,2)	𝑋^22−𝑋1−3
𝑆(1,1)	𝑋1𝑋2+2𝑋1+2𝑋2+4
𝑆(2,0)	𝑋^21−𝑋^32+4𝑋1𝑋2+7𝑋1+10𝑋2+11
𝑆(1,2)	𝑋1𝑋^22−𝑋^21+𝑋^22−4𝑋1−3
𝑆(2,1)	𝑋^21𝑋2−𝑋^42+3𝑋1𝑋^22+2𝑋^21−𝑋^32+10𝑋1𝑋2+9𝑋^22+9𝑋1+19𝑋2+10
𝑆(2,2)	𝑋^21𝑋^22−𝑋^52−𝑋^31+4𝑋1𝑋^32−3𝑋^21𝑋2+6𝑋1𝑋^22−9𝑋^21+12𝑋^32−18𝑋1𝑋2+9𝑋^22−27𝑋1−27𝑋2−27