Theoretical analysis demonstrates the derivation of Fischer matrices in an affine subgroup of GO(5,3), enabling the complete construction of its character table.
Key Points
Apply Clifford-Fischer theory to compute the Fischer matrices and construct the full character table of the affine subgroup 3^3:GO(3,3) within the general orthogonal group GO(5,3).
Examined the maximal embedding of the affine subgroup 3^3:GO(3,3) in O(5,3):2 and the full symplectic group Sp(4,3).
Calculated the Fischer matrices of the affine extension using the Clifford-Fischer theoretical framework.
Successfully derived the Fischer matrices for the affine subgroup 3^3:GO(3,3).
Constructed the complete character table of 3^3:GO(3,3) through the combination of Fischer matrices and inertia factor character tables.