On multiplier systems and theta functions of half-integral weight for the Hilbert modular group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="normal">SL</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="fraktur">o</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>