  We study the characteristic polynomials of both the Gaussian Orthogonal and
Symplectic Ensembles. We show that for both ensembles, powers of the absolute
value of the characteristic polynomials converge in law to Gaussian
multiplicative chaos measures after normalization for sufficiently small real
powers. The main tool is a new asymptotic relation between the fractional
moments of the absolute characteristic polynomials of Gaussian Orthogonal,
Unitary, and Symplectic Ensembles.
