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Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the matrix--valued $SL(2,R)$ formulation and effectively reduces the construction of the Geroch group to the corresponding problem for the vacuum Einstein equations. An infinite hierarchy of potentials is introduced in terms of $2\times 2$ real symmetric matrices generalizing the scalar hierarchy of Kinnersley--Chitre known for the vacuum Einstein equations.

Geroch—Kinnersley—Chitre Group for Dilaton—Axion Gravity