### Abstract

We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as SU(6, 2) covariant bases. E_{8(-24)} has E _{7}×SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d = 3. For the corresponding U-duality group E_{8(8)} of the maximal supergravity theory the minimal realization was given in [1], The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E_{8(-24)} and E_{8(8)}. By further truncation one can obtain the minimal unitary realizations of all the groups of the "Magic Triangle". We give explicitly the minimal unitary realizations of the exceptional subgroups of E_{8(-24)} as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups as defined in [2].

Original language | English (US) |
---|---|

Pages (from-to) | 381-407 |

Number of pages | 27 |

Journal | Journal of High Energy Physics |

Issue number | 1 |

State | Published - Jan 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*, (1), 381-407.

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*Journal of High Energy Physics*, no. 1, pp. 381-407.

**Minimal unitary realizations of exceptional U-duality groups and their subgroups as quasiconformal groups.** / Günaydin, Murat; Pavlyk, Oleksandr.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Minimal unitary realizations of exceptional U-duality groups and their subgroups as quasiconformal groups

AU - Günaydin, Murat

AU - Pavlyk, Oleksandr

PY - 2005/1/1

Y1 - 2005/1/1

N2 - We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E8(-24) in SU*(8) as well as SU(6, 2) covariant bases. E8(-24) has E 7×SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d = 3. For the corresponding U-duality group E8(8) of the maximal supergravity theory the minimal realization was given in [1], The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E8(-24) and E8(8). By further truncation one can obtain the minimal unitary realizations of all the groups of the "Magic Triangle". We give explicitly the minimal unitary realizations of the exceptional subgroups of E8(-24) as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups as defined in [2].

AB - We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E8(-24) in SU*(8) as well as SU(6, 2) covariant bases. E8(-24) has E 7×SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d = 3. For the corresponding U-duality group E8(8) of the maximal supergravity theory the minimal realization was given in [1], The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E8(-24) and E8(8). By further truncation one can obtain the minimal unitary realizations of all the groups of the "Magic Triangle". We give explicitly the minimal unitary realizations of the exceptional subgroups of E8(-24) as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups as defined in [2].

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UR - http://www.scopus.com/inward/citedby.url?scp=24944501653&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:24944501653

SP - 381

EP - 407

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

ER -