Unfolding $E_{11}$

We work out the unfolded formulation of the fields in the non-linear realisation of E_{11} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>11</mml:mn> </mml:msub> </mml:math> . Using the connections in this formalism, we propose, at the linearised level, an infinite number of first-order duality relations between the dual fields in E_{11} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>11</mml:mn> </mml:msub> </mml:math> . In this way, we introduce extra fields that do not belong to E_{11} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>11</mml:mn> </mml:msub> </mml:math> and we investigate their origin. The equations of motion of the fields are obtained by taking derivatives and higher traces of the duality relations.