THESIS
2022
Abstract
In this thesis, we discuss three works related to automorphic forms on Kac-Moody
groups. In the first work, we first give a symplectic realization of twisted loop
groups of type A
n(2) (n ≥ 2), then we compute the corresponding Weil representations,
and realize this representation as a representation of the metaplectic cover
of the corresponding Kac-Moody group constructed by Patnaik-Puskas in [PP].
In the second work, we computed the theta lifting of of the (GL
n,GL
n) dual pair
of loop groups, starting from a function induced by a classical cuspidal automorphic
form on GL
n, and we explain the result as a certain Eisenstein series induced
from a maximal parabolic subgroup of the loop GL
n group. In the third work,
we proved that the inverse of the Kac-Moody correction factor, a certain fo...[
Read more ]
In this thesis, we discuss three works related to automorphic forms on Kac-Moody
groups. In the first work, we first give a symplectic realization of twisted loop
groups of type A
n(2) (n ≥ 2), then we compute the corresponding Weil representations,
and realize this representation as a representation of the metaplectic cover
of the corresponding Kac-Moody group constructed by Patnaik-Puskas in [PP].
In the second work, we computed the theta lifting of of the (GL
n,GL
n) dual pair
of loop groups, starting from a function induced by a classical cuspidal automorphic
form on GL
n, and we explain the result as a certain Eisenstein series induced
from a maximal parabolic subgroup of the loop GL
n group. In the third work,
we proved that the inverse of the Kac-Moody correction factor, a certain formal
power series associated to a Kac-Moody root system, converges to a holomorphic
function on the interior of the complexified Tits cone.
Post a Comment