Related papers: Global L-packets of quasisplit $GSp(2n)$ and $GO(2…

In his monograph (2013) Arthur characterizes the L-packets of quasisplit symplectic groups and orthogonal groups. By extending his work, we characterize the L-packets for the corresponding similitude groups with desired properties. In…

Let $G \subseteq \tilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and $G_{der} = \tilde{G}_{der}$. Although the existence of L-packets is still conjectural in general, it is believed that the…

We construct the Arthur packets for symplectic and even orthogonal similitude groups over a $p$-adic field and show that they are stable and satisfy the twisted endoscopic character relations.

We consider the split special orthogonal group $\mathrm{SO}_{N}$ defined over a $p$-adic field. We determine the structure of any $L$-packet of $\mathrm{SO}_{N}$ containing a simple supercuspidal representation (in the sense of…

In this paper, for quasi-split classical groups over p-adic fields, we determine the L-packets consisting of simple supercuspidal representations and their corresponding L-parameters, under the assumption that p is not equal to 2. The key…

We define a new cohomology set for an affine algebraic group G and a multiplicative finite central subgroup Z, both defined over a local field of characteristic zero, which is an enlargement of the usual first Galois cohomology set of G. We…

In this paper, we give a simple and short proof of the uniqueness of generic representations in an $L$-packet for a quasi-split connected classical group over a non-archimedean local field.

In this paper, we give a uniform classification of the generic dual of quasi-split classical groups, their similitude counterparts, and general spin groups. As applications, for quasi-split classical groups, we show that the functorial…

Let $n$ and $k$ be positive integers such that $n$ is even. We derive new global integrals for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$ from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and…

We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex…

We give a survey on M{\oe}glin's construction of representations in the Arthur packets for $p$-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing M{\oe}glin's parametrization of elements in the Arthur packets…

In one article, the author has defined an L-group associated to a cover of a quasisplit reductive group over a local or global field. In another article, Wee Teck Gan and Fan Gao define (following an unpublished letter of the author) an…

In this note we give a self-contained proof of the following classification (up to conjugation) of subgroups of the general symplectic group of dimension n over a finite field of characteristic l, for l at least 5, which can be derived from…

We develop the local theory of the generalized doubling method for the $m$-fold central extension $Sp_{2n}^{(m)}$ of Matsumoto of the symplectic group. We define local $\gamma$-, $L$- and $\epsilon$-factors for pairs of genuine…

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \cite{Lust-Stevens} in this case, where…

Suppose that $X$ is an infinite, connected, locally finite, quasi-transitive graph with the property that every bi-infinite quasi-geodesic uniformly coarsely separates $X$ into exactly two deep pieces. We show that such an $X$ is…

We study the generalized doubling method for pairs of representations of $G\times GL_k$ where $G$ is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals, and prove that…

In a recent paper, DeBacker and Reeder construct and parameterize L-packets on pure inner forms of unramified p-adic groups, that consist of depth zero supercuspidal representations. We generalize their work to non-pure inner forms, by…

We develop a general procedure to study the combinatorial structure of Arthur packets for $p$-adic quasisplit $Sp(N)$ and $O(N)$ following the works of M{\oe}glin. This allows us to answer many delicate questions concerning the Arthur…

We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$…