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We study the minimal unitary representations of noncompact exceptional groupsthat arise as U-duality groups in extended supergravity theories. First we givethe unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as wellas SU(6,2) covariant bases. E_{8(-24)} has E_7 X SU(2) as its maximal compactsubgroup and is the U-duality group of the exceptional supergravity theory ind=3. For the corresponding U-duality group E_{8(8)} of the maximal supergravitytheory the minimal realization was given in hep-th/0109005. The minimal unitaryrealizations of all the lower rank noncompact exceptional groups can beobtained by truncation of those of E_{8(-24)} and E_{8(8)}. By furthertruncation one can obtain the minimal unitary realizations of all the groups ofthe "Magic Triangle". We give explicitly the minimal unitary realizations ofthe exceptional subgroups of E_{8(-24)} as well as other physically interestingsubgroups. These minimal unitary realizations correspond, in general, to thequantization of their geometric actions as quasi-conformal groups as defined inhep-th/0008063.Comment: 28 pages. Latex commands removed from the abstract for the arXiv. No  changes in the manuscrip

Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups