Jing-Song Huang
The endoscopic transfer factor is expressed as difference of characters for the even and odd parts of the spin modules, or Dirac index of the trivial representation. The lifting of tempered characters in terms of index of Dirac cohomology is calculated explicitly.
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We formulate the transfer factor of character lifting from orthogonal groups to symplectic groups by Adams in the framework of symplectic Dirac cohomology for the Lie superalgebras and the Rittenberg-Scheunert correspondence of representations of the Lie superalgebra $\fro\frsp(1|2n)$ and the Lie algebra $\fro(2n+1)$. This leads to formulation of a direct lifting of characters from the linear symplectic group $Sp(2n,\bbR)$ to its nonlinear covering metaplectic group $Mp(2n,\bbR)$.
Homotopy liftings and Hochschild cohomology of some twisted tensor products
该研究利用Volkov的同伦提升方法，给出代数张量积及双特征扭曲张量积的Hochschild上同调同构结论的新证明，展现了同伦提升的理论应用价值。
Jacquet modules of Tate cohomology and base change lifting
本文在非阿基米德局部域的连通约化群框架下，证明了Treumann-Venkatesh关于Tate上同调群为有限长表示的猜想，给出GL_n深度0尖点表示基变更提升情形的显式计算，拓展至非尖点情形并研究了Sp_4的相关Tate上同调。
Dirac cohomology and $Θ$-correspondence for complex dual pairs
本文研究复约化对偶对下 Dirac 上同调在 Howe 的 $\Theta$-对应中的行为，刻画了具有非零 Dirac 上同调的 Harish-Chandra 模，其 $\Theta$-提升仍保持非零，并显式计算了提升后的 Dirac 上同调。
In this paper, we obtained character formulas of irreducible unitary representations of $U(n, n+1)$ by using Howe's correspondence and the Cauchy--Harish-Chandra integral. The representations of $U(n, n+1)$ we are dealing with are obtained from a double lifting of a representation of $U(1)$ via the dual pairs $(U(1), U(1, 1))$ and $(U(1, 1), U(n, n+1))$.
Given a connected reductive group $\tilde{G}$ over a finite field $k$, and a semisimple $k$-automorphism $\varepsilon$ of $\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $\varepsilon$-fixed points. Then there exists a lifting from packets of representations of $G(k)$ to packets for $\tilde{G}(k)$. In the case of Deligne-Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.
One aspect of the Langlands program for linear groups is lifting of characters, which relates virtual representations on a group $G$ with those on an endoscopic group for $G$. The goal of this paper is to extend this theory to nonlinear two-fold covers of real groups in the simply laced case. Suppose $\tG$ is a two-fold cover of a real reductive group $G$. The main result is that there is an operation, denoted $\Lift_G^{\tG}$, taking a stable virtual character of $G$ to 0 or a virtual genuine character of $\tG$, and $\Lift_G^{\tG}(Θ_π)$ may be explicitly computed if $π$ is a stable sum of stan…
Lifting semisimple characters of $p$-adic types from fixed-point subgroups
本文研究了从固定点子群提升 $p$-adic 类型的半单特征，并通过提升 Kim-Yu 数据来实现这一过程。
On the classicality theorem and its applications to the automorphy lifting theorem and the Breuil-M$\mathrm{\acute{e}}$zard conjecture in some $\mathrm{GL}_2(\mathbb{Q}_{p^2})$ cases
本文研究了某些 GL₂(Q_{p²}) 情况下的经典性定理及其应用，包括自守提升定理和 Breuil-Mézard 猜想。
We compute the characters of simple supercuspidal representations of twisted GL(2n) and standard SO(2n+1) over a p-adic field. Comparing them by the endoscopic character relation, we determine the liftings of simple supercuspidal representations of SO(2n+1) to GL(2n), under the assumption that p is not equal to 2.
Let U(N) be the quasi-split unitary group in N variables for a quadratic unramified extension of p-adic fields. We compute the characters of simple supercuspidal representations of twisted GL(N) and U(N). Comparing them by the endoscopic character relation, we determine the liftings of simple supercuspidal representations of U(N) to GL(N), under the assumption that p is not equal to 2.
Following the paradigm of \cite{MR3117742}, we are going to explore the stable transfer factors for $\mathrm{Sym}^{n}$ lifting from $\mathrm{GL}_{2}$ to $\mathrm{GL}_{n+1}$ over any local fields $F$ of characteristic zero with residue characteristic not equal to $2$. When $F=\mathbb{C}$ we construct an explicit stable transfer factor for any $n$. When $n$ is odd, we provide a reduction formula, reducing the question to the construction of the stable transfer factors when the $L$-morphism is the diagonal embedding from $\mathrm{GL}_{2}(\mathbb{C})$ to finitely many copies of $\mathrm{GL}_{2}(\m…
We study the theta lifting for real unitary groups and completely determine the theta lifts of discrete series representations. In particular, we show that these theta lifts can be expressed as cohomologically induced representations in the weakly fair range. This extends a result of J.-S. Li in the case of discrete series representations with sufficiently regular infinitesimal character, whose theta lifts can be expressed as cohomologically induced representations in the good range.
We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as cohomologically induced representations in the weakly fair range. This extends a result of J.-S. Li in the case of discrete series representations with sufficiently regular infinitesimal character, whose theta lifts can be expressed as cohomologically induced representations in the good range.
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