On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems

Table 1

The structure of functions and dictating the entries of matrices and , which reflect the respective symmetry groups. The s are the Fourier coefficients of the symbol of . Note that, for all symmetry classes other than , and thus .

Classical compact group	Structure of matrices	Matrix entries
			,
		if
		if
		either
		or
		,
		,
		,
		,