@article{SIGMA_2021_17_a21,
author = {Guilherme F. Almeida},
title = {The {Differential} {Geometry} of the {Orbit} {Space} of {Extended} {Affine} {Jacobi} {Group} $A_1$},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2021},
volume = {17},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a21/}
}
TY - JOUR AU - Guilherme F. Almeida TI - The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$ JO - Symmetry, integrability and geometry: methods and applications PY - 2021 VL - 17 UR - http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a21/ LA - en ID - SIGMA_2021_17_a21 ER -
Guilherme F. Almeida. The Differential Geometry of the Orbit Space of Extended Affine Jacobi Group $A_1$. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a21/
[1] Almeida G. F., Differential geometry of orbit space of extended affine Jacobi group $A_n$, arXiv: 2004.01780 | MR
[2] Bertola M., “Frobenius manifold structure on orbit space of Jacobi groups. I”, Differential Geom. Appl., 13 (2000), 19–41 | DOI | MR | Zbl
[3] Bertola M., “Frobenius manifold structure on orbit space of Jacobi groups. II”, Differential Geom. Appl., 13 (2000), 213–233 | DOI | MR | Zbl
[4] Bourbaki N., “Lie groups and Lie algebras”, Elements of Mathematics (Berlin), Chapters 4–6, Springer-Verlag, Berlin, 2002 | MR | Zbl
[5] Cutimanco M., Shramchenko V., “Explicit examples of Hurwitz Frobenius manifolds in genus one”, J. Math. Phys., 61 (2020), 013501, 20 pp. | DOI | MR | Zbl
[6] Dubrovin B., “Geometry of $2$D topological field theories”, Integrable Systems and Quantum Groups (Montecatini Terme, 1993), Lecture Notes in Math., 1620, Springer, Berlin, 1996, 120–348, arXiv: hep-th/9407018 | DOI | MR | Zbl
[7] Dubrovin B., “Differential geometry of the space of orbits of a Coxeter group”, Surveys in Differential Geometry: Integrable Systems, Surv. Differ. Geom., 4, Int. Press, Boston, MA, 1998, 181–211, arXiv: hep-th/9303152 | DOI | MR
[8] Dubrovin B., “Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions”, New Trends in Mathematical Physics, Springer, Dordrecht, 2009, 231–276 | DOI | MR | Zbl
[9] Dubrovin B., Strachan I. A.B., Zhang Y., Zuo D., “Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau–Ginzburg superpotentials”, Adv. Math., 351 (2019), 897–946, arXiv: 1510.08690 | DOI | MR | Zbl
[10] Dubrovin B., Zhang Y., “Extended affine Weyl groups and Frobenius manifolds”, Compositio Math., 111 (1998), 167–219, arXiv: hep-th/9611200 | DOI | MR | Zbl
[11] Dubrovin B., Zhang Y., Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov–Witten invariants, arXiv: math.DG/0108160
[12] Eichler M., Zagier D., “The theory of Jacobi forms”, Progress in Mathematics, 55, Birkhäuser Boston, Inc., Boston, MA, 1985 | DOI | MR | Zbl
[13] Ferapontov E. V., Pavlov M. V., Xue L., Second-order integrable Lagrangians and WDVV equations, arXiv: 2007.03768 | MR
[14] Hertling C., Multiplication on the tangent bundle, arXiv: math.AG/9910116
[15] Pavlov M. V., Tsarev S. P., “Tri-Hamiltonian structures of Egorov systems of hydrodynamic type”, Funct. Anal. Appl., 37 (2003), 32–45 | DOI | MR | Zbl
[16] Romano S., “4-dimensional Frobenius manifolds and Painleve' VI”, Math. Ann., 360 (2014), 715–751, arXiv: 1209.3959 | DOI | MR | Zbl
[17] Romano S., “Frobenius structures on double Hurwitz spaces”, Int. Math. Res. Not., 2015 (2015), 538–577, arXiv: 1210.2312 | DOI | MR | Zbl
[18] Saito K., Yano T., Sekiguchi J., “On a certain generator system of the ring of invariants of a finite reflection group”, Comm. Algebra, 8 (1980), 373–408 | DOI | MR | Zbl
[19] Shramchenko V., “Deformations of Frobenius structures on Hurwitz spaces”, Int. Math. Res. Not., 2005 (2005), 339–387, arXiv: math-ph/0408026 | DOI | MR | Zbl
[20] Strachan I. A.B., “Frobenius submanifolds”, J. Geom. Phys., 38 (2001), 285–307, arXiv: math.DG/9912081 | DOI | MR | Zbl
[21] Strachan I. A.B., “Frobenius manifolds: natural submanifolds and induced bi-Hamiltonian structures”, Differential Geom. Appl., 20 (2004), 67–99, arXiv: math.DG/0201039 | DOI | MR | Zbl
[22] Whittaker E. T., Watson G. N., A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996 | DOI | MR | Zbl
[23] Wirthmüller K., “Root systems and Jacobi forms”, Compositio Math., 82 (1992), 293–354 | MR | Zbl
[24] Zuo D., “Frobenius manifolds and a new class of extended affine Weyl groups of A-type”, Lett. Math. Phys., 110 (2020), 1903–1940, arXiv: 1905.09470 | DOI | MR | Zbl