相关论文: The non-tempered theta 10 Arthur parameter and Gro…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

We consider the local multiplicity problems of the analogy of the Ginzburg-Rallis model for the unitary group and the unitary similitude group cases. For the unitary similitude group case, by proving a local trace formula for the model, we…

The framework of generalized probabilistic theories (GPT) is a widely-used approach for studying the physical foundations of quantum theory. The standard GPT framework assumes the no-restriction hypothesis, in which the state space of a…

We study GL_2(F)-invariant periods on representations of GL_2(A), where F is a nonarchimedean local field and A/F a product of field extensions of total degree 3. For irreducible representations, a theorem of Prasad shows that the space of…

We combine $SO(10)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. We focus on the case where the three fermion…

Let $G=\mathbf{G}(\mathbb{R})$ be the group of real points of a quasi-split connected reductive algebraic group defined over $\mathbb{R}$. Assume furthermore that $G$ is a classical group (symplectic, special orthogonal or unitary). We show…

The Bruhat-Tits theory is a key ingredient in the construction of irreducible smooth representations of $p$-adic reductive groups. We describe generalizations to arbitrary such representations of several results recently obtained in the…

This paper begins the project of defining Arthur packets of all unipotent representations for the $p$-adic exceptional group $G_2$. Here we treat the most interesting case by defining and computing Arthur packets with component group $S_3$.…

In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for $U(V_K)/U(V)$ for…

It is often argued that in the class of non-supersymmetric SO(10) grand unified theories there is barely any room for reconciling the lower bound on the position of the GUT scale emerging from the proton decay searches and the lower limit…

We review SO(10) grand unified theories (GUTs) in four and five dimensions (4D and 5D). The renormalizable minimal SO(10) SUSY GUT is the central theme of this review. It is very predictive and makes it possible to construct all mass…

We give an explicit construction of Arthur packets for real unitary groups by cohomological and parabolic induction and following an idea communicated to us by P. Trapa, we show that they satisfy the multiplicity one property. In…

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and…

For $\mathrm{GL}_n$ over a $p$-adic field, Cunningham and Ray proved Vogan's conjecture, that is, local Arthur packets are the same as ABV packets. They used the endoscopic theory to reduce the general case to a combinatorial lemma for…

Through combining the work of Jean-Loup Waldspurger (\cite{waldspurger10} and \cite{waldspurgertemperedggp}) and Rapha\"el Beuzart-Plessis (\cite{beuzart2015local}), we give a proof for the tempered part of the local Gan-Gross-Prasad…

We study the compatibility of Arthur's conjecture for $R$-groups in the restriction of discrete series representations from Levi subgroups of a $p$-adic group to those of its closed subgroup having the same derived group. The compatibility…

Using the theory of polarised flag type quotients, we determine mass formulae for all principally polarised supersingular abelian threefolds defined over an algebraically closed field $k$ of characteristic $p$. We combine these results with…

Let $\pi$ be an irreducible cuspidal automorphic representation of a quasi-split unitary group ${\rm U}_{\mathfrak n}$ defined over a number field $F$. Under the assumption that $\pi$ has a generic global Arthur parameter, we establish the…

We study the local theta correspondence for dual pairs of the form $\mathrm{Aut}(C)\times F_{4}$ over a $p$-adic field, where $C$ is a composition algebra of dimension 2 or 4, by restricting the minimal representation of a group of type…

In a companion paper, we formulated a global conjecture for the automorphic period integral associated to the symmetric pairs defined by unitary groups over number fields, generalizing a theorem of Waldspurger's toric period for…