Orthogonal Polynomials of Compact Simple Lie Groups

Table 9

𝐶 polynomials of 𝐶₃ split into two congruence classes #=0 and #=1.

𝐶 polynomials
#=0
𝐶(0,1,0)	𝑋2
𝐶(2,0,0)	−6−2𝑋2+𝑋^21
𝐶(1,0,1)	−2𝑋2+𝑋1𝑋3
𝐶(0,2,0)	12+8𝑋2−4𝑋^21−2𝑋1𝑋3+𝑋^22
𝐶(2,1,0)	−6𝑋2−𝑋1𝑋3−2𝑋^22+𝑋^21𝑋2
𝐶(0,0,2)	−8−8𝑋2+4𝑋^21+4𝑋1𝑋3−2𝑋^22+𝑋^23
𝐶(1,1,1)	12𝑋2−4𝑋1𝑋3+4𝑋^22−2𝑋^21𝑋2−3𝑋^23+𝑋1𝑋2𝑋3
𝐶(0,3,0)	9𝑋2+3𝑋1𝑋3+6𝑋^22−3𝑋^21𝑋2+3𝑋^23−3𝑋1𝑋2𝑋3+𝑋^32
𝐶(0,1,2)	−18𝑋2+3𝑋1𝑋3−12𝑋^22+6𝑋^21𝑋2+3𝑋^23+3𝑋1𝑋2𝑋3−2𝑋^32+𝑋2𝑋^23
#=1
𝐶(1,0,0)	𝑋1
𝐶(0,0,1)	𝑋3
𝐶(1,1,0)	−4𝑋1−3𝑋3+𝑋1𝑋2
𝐶(3,0,0)	−3𝑋1+3𝑋3−3𝑋1𝑋2+𝑋^31
𝐶(0,1,1)	4𝑋1+6𝑋3−2𝑋1𝑋2+𝑋2𝑋3
𝐶(2,0,1)	−9𝑋3−2𝑋2𝑋3+𝑋^21𝑋3
𝐶(1,2,0)	12𝑋1−3𝑋3+9𝑋1𝑋2−4𝑋^31−𝑋2𝑋3−2𝑋^21𝑋3+𝑋1𝑋^22
𝐶(1,0,2)	−12𝑋1−6𝑋3−6𝑋1𝑋2+4𝑋^31−𝑋2𝑋3+4𝑋^21𝑋3−2𝑋1𝑋^22+𝑋1𝑋^23
𝐶(0,2,1)	27𝑋3+12𝑋2𝑋3−6𝑋^21𝑋3−2𝑋1𝑋^23+𝑋^22𝑋3
𝐶(0,0,3)	−27𝑋3−18𝑋2𝑋3+9𝑋^21𝑋3+6𝑋1𝑋^23−3𝑋^22𝑋3+𝑋^33