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Jia-Jun Ma

Publications and source records attributed to Jia-Jun Ma.

17 recordsLinked to original sources
arXiv2026

Arithmetic Wavefront Set and Microlocal Structure of Harish-Chandra Character

In this paper, we establish in Theorem 1.2 the reciprocity of wavefront sets for irreducible admissible representations $\pi$ of classical groups $G$ over any local field $F$ of characteristic zero if $\pi$ has a generic local $L$-parameter. Over archimedean local fields, based on the progress made in our previous work (arXiv:2207.04700), we prove in Theorem 1.5 that for an irreducible Casselman--Wallach representation $\pi$ with a generic local $L$-parameter, the Wavefront Set Conjecture (arXiv:2207.04700, Conjecture 1.2) and its refinement (Conjecture 1.1) hold for the arithmetic wavefront set ${\mathrm{WF}}_{\mathrm{ari}}(\pi)$ as defined by the associated enhanced local $L$-parameter of $\pi$ and the wavefront set ${\mathrm{WF}}_{\mathrm{tr}}(\pi)$ defined by the Harish--Chandra distribution character $\Theta_\pi$ of $\pi$. Hence the microlocal structure of $\Theta_\pi$ is completely determined by the arithmetic information carried by the enhanced local $L$-parameter of $\pi$. The relations with the algebraic wavefront set ${\mathrm{WF}}_{\mathrm{wm}}(\pi)$ defined by the degenerate Whittaker models are extensively discussed by means of the composition law (Theorem 3.4) over all local fields of characteristic zero. Under Conjecture 1.3, the Wavefront Set Conjecture is fully established over archimedean local fields. As a consequence, we prove a refinement of Vogan's maximal-orbit principle (Theorem 1.7).

math.RT↗
arXiv2025

Theta correspondence and Springer correspondence

In this paper, we obtain an explicit formula for the theta correspondence of unipotent principal-series representations between an even orthogonal and a symplectic group or between general linear groups over a finite field. The formula is in terms of the Springer correspondence. Along the way we prove general results about module categories of Hecke categories arising from spherical varieties, and give a similar formula for the multiplicities of the unipotent principal series representations in the function space of the spherical variety in terms of relative Springer theory.

math.RT↗
arXiv2025

SiCmiR Atlas: Single-Cell miRNA Landscapes Reveals Hub-miRNA and Network Signatures in Human Cancers

microRNA are pivotal post-transcriptional regulators whose single-cell behavior has remained largely inaccessible owing to technical barriers in single-cell small-RNA profiling. We present SiCmiR, a two-layer neural network that predicts miRNA expression profile from only 977 LINCS L1000 landmark genes reducing sensitivity to dropout of single-cell RNA-seq data. Proof-of-concept analyses illustrate how SiCmiR can uncover candidate hub-miRNAs in bulk-seq cell lines and hepatocellular carcinoma, scRNA-seq pancreatic ductal carcinoma and ACTH-secreting pituitary adenoma and extracellular-vesicle-mediated crosstalk in glioblastoma. Trained on 6462 TCGA paired miRNA-mRNA samples, SiCmiR attains state-of-the-art accuracy on held-out cancers and generalizes to unseen cancer types, drug perturbations and scRNA-seq. We next constructed SiCmiR-Atlas, containing 632 public datasets, 9.36 million cells, 726 cell types, which is the first dedicated database of single-cell mature miRNA expression--providing interactive visualization, biomarker identification and cell-type-resolved miRNA-target networks. SiCmiR transforms bulk-derived statistical power into a single-cell view of miRNA biology and provides a community resource SiCmiR Atlas for biomarker discovery. SiCmiR Atlas is avilable at https://awi.cuhk.edu.cn/~SiCmiR/.

q-bio.GN↗
arXiv2025

Special unipotent representations of real classical groups: construction and unitarity

Let $G$ be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit $\check{\mathcal O}$ of $\check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We classify all special unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. When $\check{\mathcal O}$ has good parity in the sense of Moeglin, we construct all such representations of $G$ via the method of theta lifting. As a consequence of the construction and the classification, we conclude that all special unipotent representations of $G$ are unitarizable, as predicted by the Arthur-Barbasch-Vogan conjecture. We also determine precise structure of the associated cycles of special unipotent representations of $G$. The paper is the second in a series of two papers on the classification of special unipotent representations of real classical groups.

math.RT↗
arXiv2025

Special unipotent representations of real classical groups: counting and reduction

Let $G$ be a real reductive group in Harish-Chandra's class. We derive some consequences of theory of coherent continuation representations to the counting of irreducible representations of $G$ with a given infinitesimal character and a given bound of the complex associated variety. When $G$ is a real classical group (including the real metaplectic group), we investigate the set of special unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. Here $\check{\mathcal O}$ is a nilpotent adjoint orbit in the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We give a precise count for the number of special unipotent representations of $G$ attached to $\check{ \mathcal O}$. We also reduce the problem of constructing special unipotent representations attached to $\check{\mathcal O}$ to the case when $\check{\mathcal O}$ is analytically even (equivalently for a real classical group, has good parity in the sense of Mœglin). The paper is the first in a series of two papers on the classification of special unipotent representations of real classical groups.

math.RT↗
arXiv2024

Associated varieties of minimal highest weight modules

Let $\mathfrak{g}$ be a complex simple Lie algebra. A simple $\mathfrak{g}$-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of this paper is a classification of minimal highest weight modules for $\\mathfrak{g}$. This classification extends the work of Joseph, which focused on categorizing minimal highest weight modules annihilated by completely prime ideals. Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties.

math.RT↗
arXiv2024

On the annihilator variety of a highest weight module for classical Lie algebras

Let $\mathfrak{g}$ be a classical complex simple Lie algebra. Let $L(λ)$ be a highest weight module of $\mathfrak{g}$ with highest weight $λ-ρ$, where $ρ$ is half the sum of positive roots. The associated variety of the annihilator ideal of $L(λ)$ is called the annihilator variety of $L(λ)$.It is known that the annihilator variety of any highest weight module $L(λ)$ is the Zariski closure of a nilpotent orbit in $\mathfrak{g}^*$. But in general, this nilpotent orbit is not easy to describe for a given highest weight module $L(λ)$. In this paper, we will give some simple formulas to characterize this unique nilpotent orbit appearing in the annihilator variety of a highest weight module for classical Lie algebras. Our formulas are given by introducing two algorithms, i.e., bipartition algorithm and partition algorithm. To get a special or metaplectic special partition from a domino type partition, we define the H-algorithm based on the Robinson-Schensted insertion algorithm. By using this H-algorithm, we can easily determine this nilpotent orbit from the information of $λ$.

math.RT↗
arXiv2023

Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups

In this paper, we deduce explicit multiplicity formulas of the Fourier-Jacobi model for Deligne-Lusztig characters of finite symplectic groups, unitary groups, and general linear groups. We then apply these results to deduce the explicit depth zero local descent (à la Soudry and Tanay) for $p$-adic unitary groups. The result is a concrete example in the context of non-tempered Gan-Gross-Prasad program.

math.RT↗
arXiv2023

Genuine special unipotent representations of spin groups

We determine all genuine special unipotent representations of real spin groups and quaternionic spin groups, and show in particular that all of them are unitarizable. We also show that there are no genuine special unipotent representations of complex spin groups.

math.RT↗
arXiv2023

On the notion of metaplectic Barbasch-Vogan duality

In analogy with the Barbasch-Vogan duality for real reductive linear groups, we introduce a duality notion useful for the representation theory of the real metaplectic groups. This is a map on the set of nilpotent orbits in a complex symplectic Lie algebra, whose range consists of the so-called metaplectic special nilpotent orbits. We relate this duality notion with the theory of primitive ideals and extend the notion of special unipotent representations to the real metaplectic groups. We also interpret the duality map in terms of double cells of Weyl group representations.

math.RT↗
arXiv2022

Generic Hecke algebra and theta correspondence over finite fields

We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for type I dual pairs over finite fields. For the product of the pair of Hecke algebras under consideration, we show that there is a generic Hecke algebra module whose specializations at prime powers give the Hecke algebra modules and whose specialization at $1$ can be explicitly described. As an application, we prove the conservation relation on the first occurrence indices for all irreducible representations. As another application, we generalize the results of Aubert-Michel-Rouquier and Pan on theta correspondence between the Harish-Chandra series.

math.RT↗
arXiv2019

Nilpotent orbits of orthogonal groups over $p$-adic fields, and the DeBacker parametrization

For local non-archimedean fields $k$ of sufficiently large residual characteristic, we explicitly parametrize and count the rational nilpotent adjoint orbits in each algebraic orbit of orthogonal and special orthogonal groups. We separately give an explicit algorithmic construction for representatives of each orbit. We then, in the general setting of groups $\mathrm{GL}_n(D)$, $\mathrm{SL}_n(D)$ (where $D$ is a central division algebra over $k$) or classical groups, give a new characterisation of the "building set" (defined by DeBacker) of an $\mathfrak{sl}_2(k)$-triple in terms of the building of its centralizer. Using this, we prove our construction realizes DeBacker's parametrization of rational nilpotent orbits via elements of the Bruhat-Tits building.

math.GR↗
arXiv2016

On two questions concerning representations distinguished by the Galois involution

Let E/F be a quadratic extension of non-archimedean local fields of characteristic 0. In this paper, we investigate two approaches which attempt to describe the smooth irreducible representations of GL(n,E) that are distinguished by its subgroup GL(n,F). One relates this class to representations which come as base change lifts from a quasi-split unitary group F, while another deals with a certain symmetry condition. By characterizing the union of images of the base change maps we show that these two approaches are closely related. Using this observation, we are able to prove a statement relating base change and distinction for ladder representations. We then produce a wide family of examples in which the symmetry condition does not impose GL(n,F)-distinction, and thus exhibit the limitations of these two approaches.

math.RT↗
arXiv2014

Semi-loss-tolerant strong quantum coin-flipping protocol using quantum non-demolition measurement

In this paper, we present a semi-loss-tolerant strong quantum coin-flipping (QCF) protocol with the best bias of 0.3536. Our manuscript applies Quantum non-demolition (QND) measurement to quantum coin-flipping protocol. Furthermore, a single photon as a single qubit is used to avoid the difficult implementation of EPR resources. We also analyze the security of our protocol obtaining the best result among all coin-flipping protocols considering loss. A semi-loss-tolerant Quantum Dice Rolling (QDR) protocol is first proposed, and the security of corresponding three-party QDR is analyzed to better demonstrate the security of our QCF.

quant-ph↗
arXiv2013

Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules.

math.RT↗
arXiv2012

Semi-Loss-Tolerant Strong Coin Flipping Protocol Using EPR Pairs

In this paper, we present a quantum strong coin flipping protocol. In this protocol, an EPR pair and a quantum memory storage are made use of, and losses in the quantum communication channel and quantum memory storage are all analyzed. We obtain the bias in the fair scenario as a function of $p$, where $p$ is the probability that the particle in Bob's quantum memory storage is lost, which means our bias varies as the degree of losses in the quantum memory storage changes. Therefore we call our protocol semi-loss-tolerant. We also show that the bias decreases with decreasing $p$. When $p$ approaches 0, the bias approaches 0.3536, which is less than that of all the previous loss-tolerant protocols. Details of both parties' optimal cheating strategies are also given and analyzed. What's more, experimental feasibility is discussed and demonstrated. Compared with previous qubit-based loss-tolerant SCF protocols, we introduce the EPR pair to keep our protocol loss-tolerant while trying to push down the bias. In addition, a quantum memory storage is used and the losses in it has been taken into account. We obtain the bias in the fair scenario as a function of $p$, where $p$ is the probability that the particle in Bob's quantum memory storage is lost, which means our bias varies as the degree of losses in the quantum memory storage changes. We also show that the bias decreases with decreasing $p$. When $p$ approaches 0, the bias approaches 0.3536, which is less than that of all the previous loss-tolerant protocols. Details of both parties' optimal cheating strategies are also given and analyzed. Besides, experimental feasibility is discussed and demonstrated.

quant-ph↗