Orthogonal Polynomials of Compact Simple Lie Groups

Table 8

𝐶 polynomials of 𝐵₃ split into two congruence classes #=0 and #=1.

𝐶 polynomials
#=0
𝐶(1,0,0)	𝑋1
𝐶(0,1,0)	𝑋2
𝐶(2,0,0)	−6−2𝑋2+𝑋^21
𝐶(0,0,2)	−8−4𝑋1−2𝑋2+𝑋^23
𝐶(1,1,0)	24+8𝑋1+6𝑋2−3𝑋^23+𝑋1𝑋2
𝐶(1,0,2)	−8𝑋1−2𝑋2−4𝑋^21−2𝑋1𝑋2+𝑋1𝑋^23
𝐶(3,0,0)	−24−15𝑋1−6𝑋2+𝑋^23−3𝑋1𝑋2+𝑋^31
𝐶(0,2,0)	12+16𝑋1+8𝑋2+4𝑋^21+4𝑋1𝑋2−2𝑋1𝑋^23+𝑋^22
𝐶(0,1,2)	−48−20𝑋1−20𝑋2+6𝑋^23−6𝑋1𝑋2−2𝑋^22+𝑋2𝑋^23
𝐶(2,1,0)	8𝑋1−6𝑋2+4𝑋^21+2𝑋1𝑋2−𝑋1𝑋^23−2𝑋^22+𝑋^21𝑋2
#=1
𝐶(0,0,1)	𝑋3
𝐶(1,0,1)	−3𝑋3+𝑋1𝑋3
𝐶(0,1,1)	3𝑋3−2𝑋1𝑋3+𝑋2𝑋3
𝐶(0,0,3)	−9𝑋3−3𝑋1𝑋3−3𝑋2𝑋3+𝑋^33
𝐶(2,0,1)	−3𝑋3−𝑋1𝑋3−2𝑋2𝑋3+𝑋^21𝑋3
𝐶(1,1,1)	30𝑋3+12𝑋1𝑋3+8𝑋2𝑋3−3𝑋^33−2𝑋^21𝑋3+𝑋1𝑋2𝑋3