2013/12/12 by Philipp Fleig, Fleig, Philipp, Axel Kleinschmidt +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Automorphic form #Black Holes and Theoretical Physics #Degenerate energy levels #Eisenstein series #FOS: Mathematics #FOS: Physical sciences #Fourier series #High Energy Physics - Theory (hep-th) #Instanton #Mathematical analysis #Mathematical physics #Mathematics #Modular form #Number Theory (math.NT) #Physics #Pure mathematics #Quantum mechanics #Representation Theory (math.RT) #Series (stratigraphy) #Unipotent #hep-th #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.1312.3643
published in arXiv (Cornell University) (Cornell University) · 62 pages. Journal version
openalex publication_date 2013/12/12 · arxiv created 2015/03/02 · arxiv updated 2015/03/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/05
Motivated by string theory scattering amplitudes that are invariant under a\ndiscrete U-duality, we study Fourier coefficients of Eisenstein series on\nKac-Moody groups. In particular, we analyse the Eisenstein series on E9(R),\nE10(R) and E11(R) corresponding to certain degenerate principal\nseries at the values s=3/2 and s=5/2 that were studied in 1204.3043. We show\nthat these Eisenstein series have very simple Fourier coefficients as expected\nfor their role as supersymmetric contributions to the higher derivative\ncouplings R4 and \∂4 R4 coming from 1/2-BPS and 1/4-BPS\ninstantons, respectively. This suggests that there exist minimal and\nnext-to-minimal unipotent automorphic representations of the associated\nKac-Moody groups to which these special Eisenstein series are attached. We also\nprovide complete explicit expressions for degenerate Whittaker vectors of\nminimal Eisenstein series on E6(R), E7(R) and E8(R) that have not\nappeared in the literature before.\n