Orthogonal Polynomials of Compact Simple Lie Groups

Table 1

The irreducible 𝐶 and 𝑆 polynomials of 𝐴₁ of degrees up to 8.

𝐶 polynomials		𝑆 polynomials
#=0		#=0
𝐶2	𝑋^2−2	𝑆0	1
𝐶4	𝑋^4−4𝑋^2+2	𝑆2	𝑋^2−1
𝐶6	𝑋^6−6𝑋^4+9𝑋^2−2	𝑆4	𝑋^4−3𝑋^2+1
𝐶8	𝑋^8−8𝑋^6+20𝑋^4−16𝑋^2+2	𝑆6	𝑋^6−5𝑋^4+6𝑋^2−1
#=1		#=1
𝐶1	𝑋	𝑆1	𝑋
𝐶3	𝑋^3−3𝑋	𝑆3	𝑋^3−2𝑋
𝐶5	𝑋^5−5𝑋^3+5𝑋	𝑆5	𝑋^5−4𝑋^3+3𝑋
𝐶7	𝑋^7−7𝑋^5+14𝑋^3−7𝑋	𝑆7	𝑋^7−6𝑋^5+10𝑋^3−4𝑋