论Kac-Moody Eisenstein级数的收敛性

Entirety of certain cuspidal Eisenstein series on Kac--Moody groups

Let $G$ be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on $G$ induced from unramified cusp forms on finite-dimensional Levi subgroups of maximal parabolic subgroups. Under a natural condition on maximal parabolic subgroups, we prove that the cuspidal Eisenstein series are entire on the full complex plane.

函数域上 Kac--Moody 艾森斯坦级数的收敛性

Convergence of Kac--Moody Eisenstein Series over a function field

该研究证明函数域上可对称化Kac--Moody群的艾森斯坦级数在自然域内处处收敛，其方法异于无法直接推广的仿射情形，且较实数域结果无需根系额外条件。

Eisenstein series on rank 2 hyperbolic Kac--Moody groups

We define Eisenstein series on rank 2 hyperbolic Kac--Moody groups over R, induced from quasi--characters. We prove convergence of the constant term and hence the almost everywhere convergence of the Eisenstein series. We define and calculate the degenerate Fourier coefficients. We also consider Eisenstein series induced from cusp forms and show that these are entire functions.

Metaplectic Covers of Kac-Moody Groups and Whittaker Functions

Starting from some linear algebraic data (a Weyl-group invariant bilinear form) and some arithmetic data (a bilinear Steinberg symbol), we construct a cover of a Kac-Moody group generalizing the work of Matsumoto. Specializing our construction over non-archimedean local fields, for each positive integer n we obtain the notion of $n$-fold metaplectic covers of Kac-Moody groups. In this setting, we prove a Casselman-Shalika type formula for Whittaker functions.

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

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 1204.3043. 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 $\partial^{4} R^4$ coming from 1/2-BPS and 1/4-BP…

Kac-Moody斐波那契序列

Kac--Moody Fibonacci sequences

本文研究了通过Kac-Moody代数根格生成无限整数序列的方法，并计算了部分序列的前二十项。