### Abstract

For G = G(R), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K\G using the Chevalley generators and the Steinberg presentation. When K\G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(Z) on K\G. We give explicit results for the action of the discrete U-duality groups SL_{2}(Z) and E_{7}(Z) on the scalar cosets SO(2)\SL_{2}(R) and [SU(8)/{± Id}]\E_{7(+7)}(R) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.

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

Article number | 103501 |

Journal | Journal of Mathematical Physics |

Volume | 56 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 2015 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*56*(10), [103501]. https://doi.org/10.1063/1.4929538

**Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories.** / Carbone, Lisa; Murray, Scott H.; Sati, Hisham.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 56, no. 10, 103501. https://doi.org/10.1063/1.4929538

}

TY - JOUR

T1 - Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories

AU - Carbone, Lisa

AU - Murray, Scott H.

AU - Sati, Hisham

PY - 2015/1/1

Y1 - 2015/1/1

N2 - For G = G(R), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K\G using the Chevalley generators and the Steinberg presentation. When K\G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(Z) on K\G. We give explicit results for the action of the discrete U-duality groups SL2(Z) and E7(Z) on the scalar cosets SO(2)\SL2(R) and [SU(8)/{± Id}]\E7(+7)(R) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.

AB - For G = G(R), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K\G using the Chevalley generators and the Steinberg presentation. When K\G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(Z) on K\G. We give explicit results for the action of the discrete U-duality groups SL2(Z) and E7(Z) on the scalar cosets SO(2)\SL2(R) and [SU(8)/{± Id}]\E7(+7)(R) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.

UR - http://www.scopus.com/inward/record.url?scp=84943162697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943162697&partnerID=8YFLogxK

U2 - 10.1063/1.4929538

DO - 10.1063/1.4929538

M3 - Article

VL - 56

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 10

M1 - 103501

ER -