اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn $(chi,b)$-factors of cuspidal automorphic representations of unitary groups II
60
0
0.0
(
0
)
تأليف
Chenyan Wu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We derive a precise relation of poles of Eisenstein series associated to the cuspidal datum $chiotimessigma$ and lowest occurrence of theta lifts of a cuspidal automorphic representation $sigma$ of a unitary group, where $chi$ is conjugate self-dual character. We also give a refined result on non-vanishing of periods of Eisenstein series and first occurrence of theta lifts. This gives constraints on existence of $(chi,b)$-factors in the global $A$-parameter of $sigma$.
قيم البحث
اقرأ أيضاً
Following the idea of [GJS09] for orthogonal groups, we introduce a new family of period integrals for cuspidal automorphic representations $sigma$ of unitary groups and investigate their relation with the occurrence of a simple global Arthur paramet
er $(chi,b)$ in the global Arthur parameter $psi_sigma$ associated to $sigma$, by the endoscopic classification of Arthur ([Art13], [Mok13], [KMSW14]). The argument uses the theory of theta correspondence. This can be viewed as a part of the $(chi,b)$-theory outlined in [Jia14] and can be regarded as a refinement of the theory of theta correspondences and poles of certain $L$-functions, which was outlined in [Ral91].
We give constraints on existence of $(chi,b)$-factors in the global $A$-parameter of a genuine cuspidal automorphic representation $sigma$ of the metaplectic group in terms of the invariant, lowest occurrence index, of theta lifts to odd orthogonal g
roups. We also give a refined result that relates the invariant, first occurrence index, to non-vanishing of period integral of residue of Eisenstein series associated to the cuspidal datum $chiotimessigma$. This complements our previous results for symplectic groups.
In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations $sigma$ of symplectic groups $mathrm{Sp}_{2n}(mathbb{A})$, which detects the right-most pole of the $L$-function $L(s,sigmatimes
chi)$ for some character $chi$ of $F^timesbackslashmathbb{A}^times$ of order at most $2$, and hence the occurrence of a simple global Arthur parameter $(chi,b)$ in the global Arthur parameter $psi$ attached to $sigma$. We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein series.
In this paper we analyze Fourier coefficients of automorphic forms on a finite cover $G$ of an adelic split simply-laced group. Let $pi$ be a minimal or next-to-minimal automorphic representation of $G$. We prove that any $etain pi$ is completely det
ermined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro--Shalika formula for cusp forms on $GL_n$. We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient in terms of these Whittaker coefficients. A consequence of our results is the non-existence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for $G$ of type $D_5$ and $E_8$ with a view towards applications to scattering amplitudes in string theory.
In this paper, we study top Fourier coefficients of certain automorphic representations of $mathrm{GL}_n(mathbb{A})$. In particular, we prove a conjecture of Jiang on top Fourier coefficients of isobaric automorphic representations of $mathrm{GL}_n(m
athbb{A})$ of form $$ Delta(tau_1, b_1) boxplus Delta(tau_2, b_2) boxplus cdots boxplus Delta(tau_r, b_r),, $$ where $Delta(tau_i,b_i)$s are Speh representations in the discrete spectrum of $mathrm{GL}_{a_ib_i}(mathbb{A})$ with $tau_i$s being unitary cuspidal representations of $mathrm{GL}_{a_i}(mathbb{A})$, and $n = sum_{i=1}^r a_ib_i$. Endoscopic lifting images of the discrete spectrum of classical groups form a special class of such representations. The result of this paper will facilitate the study of automorphic forms of classical groups occurring in the discrete spectrum.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
