Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors

被引：14

作者：

Fleig, Philipp ^{[1
]}

Kleinschmidt, Axel ^{[2
,3
]}

Persson, Daniel ^{[4
]}

机构：

[1] Free Univ Berlin, Inst Theoret Phys, DE-14195 Berlin, Germany

[2] Albert Einstein Inst, Max Planck Inst Gravitat Phys, DE-14476 Potsdam, Germany

[3] Int Solvay Inst, BE-1050 Brussels, Belgium

[4] Chalmers Univ Technol, S-41296 Gothenburg, Sweden

来源：

COMMUNICATIONS IN NUMBER THEORY AND PHYSICS | 2014年 / 8卷 / 01期

关键词：

U-DUALITY; UNIPOTENT ELEMENTS; REPRESENTATIONS; FORMULA;

D O I：

10.4310/CNTP.2014.v8.n1.a2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups. In particular, we analyse the Eisenstein series on E-9(R), E-10 (R) and E-11 (R) corresponding to certain degenerate principal series at the values s = 3/2 and s = 5/2 that were studied in [1]. We show that these Eisenstein series have very simple Fourier coefficients as expected for their role as supersymmetric contributions to the higher derivative couplings R-4 and partial derivative(4)-R-4 coming from 1/2-BPS and 1/4-BPS instantons, respectively. This suggests that there exist minimal and next-to-minimal unipotent automorphic representations of the associated Kac-Moody groups to which these special Eisenstein series are attached. We also provide complete explicit expressions for degenerate Whittaker vectors of minimal Eisenstein series on E-6(R), E-7(R) and E-8 (R) that have not appeared in the literature before.

引用

页码：41 / 100

页数：60