اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGeometric Waldspurger periods II
34
0
0.0
(
0
)
تأليف
Sergey Lysenko
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper we extend the calculation of the geometric Waldspurger periods from our paper math/0510110 to the case of ramified coverings. We give some applications to the study of Whittaker coefficients of the theta-lifting of automorphic sheaves from PGL_2 to the metaplectic group Mp_2, they agree with our conjectures from arXiv:1211.1596. In the process of the proof, we get some new automorphic sheaves for GL_2 in the ramified setting. We also formulate stronger conjectures about Waldspurger periods and geometric theta-lifting for the dual pair (SL_2, Mp_2).
قيم البحث
اقرأ أيضاً
Let $k$ be a local field of characteristic zero. Rankin-Selbergs local zeta integrals produce linear functionals on generic irreducible admissible smooth representations of $GL_n(k)times GL_r(k)$, with certain invariance properties. We show that up t
o scalar multiplication, these linear functionals are determined by the invariance properties.
In this paper, we introduce geometric multiplicities, which are positive varieties with potential fibered over the Cartan subgroup $H$ of a reductive group $G$. They form a monoidal category and we construct a monoidal functor from this category to t
he representations of the Langlands dual group $G^vee$ of $G$. Using this, we explicitly compute various multiplicities in $G^vee$-modules in many ways. In particular, we recover the formulas for tensor product multiplicities of Berenstein- Zelevinsky and generalize them in several directions. In the case when our geometric multiplicity $X$ is a monoid, i.e., the corresponding $G^vee$ module is an algebra, we expect that in many cases, the spectrum of this algebra is affine $G^vee$-variety $X^vee$, and thus the correspondence $Xmapsto X^vee$ has a flavor of both the Langlands duality and mirror symmetry.
Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X in the sett
ing of the quantum geometric Langlands program (for etale l-adic sheaves) in analogy with [3]. We calculate the intersection cohomology sheaf on the version of Drinfeld compactification in our twisted setting. In the case G=SL_2 we derive some results about the Fourier coefficients of our Eisenstein series. In the case of G=SL_2 and X=P^1 we also construct the corresponding theta-sheaves and prove their Hecke property.
In this paper, we give geometric realizations of Lusztigs symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of the formulas of Lusztigs symmetries.
These myh lectures at the Park City conference in 1998.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
