Orthogonal Polynomials of Compact Simple Lie Groups

Table 5

The irreducible 𝐶_(𝑎,𝑏) polynomials of 𝐺₂.

𝐶 polynomials
𝐶(1,0)	𝑋1
𝐶(0,1)	𝑋2
𝐶(0,2)	𝑋^22−2𝑋1−2𝑋2−6
𝐶(1,1)	𝑋1𝑋2−2𝑋^22+4𝑋1+2𝑋2+12
𝐶(0,3)	𝑋^32−3𝑋1𝑋2−6𝑋1−9𝑋2−12
𝐶(2,0)	𝑋^21−2𝑋^32+6𝑋1𝑋2+10𝑋1+18𝑋2+18
𝐶(1,2)	𝑋1𝑋2−2𝑋^21−3𝑋1𝑋2+2𝑋^22−10𝑋1−4𝑋2−12
𝐶(2,1)	𝑋^21𝑋2−2𝑋^42+5𝑋1𝑋^22+2𝑋^21+12𝑋1𝑋2+18𝑋^22+6𝑋1+20𝑋2
𝐶(1,3)	𝑋1𝑋^32−3𝑋^21𝑋2−8𝑋^21+4𝑋^32−21𝑋1𝑋2−34𝑋1−36𝑋2−36
𝐶(3,0)	𝑋^31−3𝑋1𝑋^32+9𝑋^21𝑋2+18𝑋^21−6𝑋^32+45𝑋1𝑋2+63𝑋1+54𝑋2+60
𝐶(2,2)	𝑋^21𝑋^22−2𝑋^52−2𝑋^31+10𝑋1𝑋^32−14𝑋^21𝑋2+2𝑋^42+6𝑋1𝑋^22−30𝑋^21+30𝑋^32−84𝑋1𝑋2−108𝑋1−124𝑋2−108
𝐶(3,1)	𝑋^31𝑋2−3𝑋1𝑋^42+8𝑋^21𝑋^22+2𝑋^52+2𝑋^31−10𝑋1𝑋^32+31𝑋^21𝑋2−6𝑋^42+34𝑋1𝑋^22+28𝑋^21−30𝑋^32+135𝑋1𝑋2+36𝑋^22+102𝑋1+164𝑋2+108
𝐶(2,3)	𝑋^21𝑋^32−2𝑋^62−3𝑋^31𝑋2+12𝑋1𝑋^42−18𝑋^21𝑋^22−6𝑋^31+21𝑋1𝑋^32−72𝑋^21𝑋2+36𝑋^42−108𝑋1𝑋^22−64𝑋^21+38𝑋^32−303𝑋1𝑋2−162𝑋^22−196𝑋1−342𝑋2−180
𝐶(3,2)	𝑋^31𝑋^22−3𝑋1𝑋^52−2𝑋^41+15𝑋^21𝑋^32−20𝑋^31𝑋2+5𝑋1𝑋^42+4𝑋^21𝑋^22−6𝑋^52−44𝑋^31+75𝑋1𝑋^32−175𝑋^21𝑋2+10𝑋^42−13𝑋1𝑋^22−238𝑋^21+90𝑋^32−480𝑋1𝑋2−34𝑋^22−484𝑋1−418𝑋2−336