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Hongfeng Zhang

Publications and source records attributed to Hongfeng Zhang.

13 recordsLinked to original sources
arXiv2026

Unitary Shimura Correspondence for Complex Classical Groups

In this paper, we construct a lifting operator from the Grothendieck group of admissible Harish-Chandra modules of $G =\mathrm{SO}_{2n}(\mathbb C)$ (resp. $\mathrm{Sp}_{2n}(\mathbb C)$) to that of genuine representations of $\mathrm{Spin}_{2n}(\mathbb C)$ (resp. $\mathrm{Spin}_{2n+1}(\mathbb C)$). We determine the lift of the sum of special unipotent representations attached to any ${}^{\vee}\mathcal O \subseteq {}^{\vee}\mathfrak g$ explicitly. In particular, the representations occurring in these lifts, if nonzero, are genuine unipotent representations of complex Spin groups and are unitary. As a consequence, the lifting operator preserves unitarity on a large class of unitary representations.

math.RT↗
arXiv2026

Stability of the smooth Casselman-Jacquet functor

We establish and prove several results for the smooth Casselman-Jacquet submodule and quotient functors for real reductive groups. In addition to exactness, surjectivity, transitivity and globalization results, we establish a stability property for the intersection of Jacquet subspaces. Our approach is based on a family of seminorms on the Casselman-Jacquet quotient module. As an application, we establish a full version of the real Bernstein-Zelevinsky filtrations for smooth Fr\'echet representations of moderate growth.

math.RT↗
arXiv2025

Archimedean Bernstein-Zelevinsky Theory and Homological Branching Laws

We develop the Bernstein-Zelevinsky theory for quasi-split real classical groups and employ this framework to establish an Euler-Poincar\'e characteristic formula for general linear groups. The key to our approach is establishing the Casselman-Wallach property for the homology of the Jacquet functor, which also provides an affirmative resolution to an open question proposed by A. Aizenbud, D. Gourevitch and S. Sahi. Furthermore, we prove the vanishing of higher extension groups for arbitrary pairs of generic representations, confirming a conjecture of Dipendra Prasad. We also utilize the Bernstein-Zelevinsky theory to establish two additional results: the Leibniz law for the highest derivative and a unitarity criterion for general linear groups. Lastly, we apply the Bernstein-Zelevinsky theory to prove the Hausdorffness and exactness of the twisted homology of split even orthogonal groups.

math.RT↗
arXiv2025

Classification of $\mathrm{GL}_{n}(\mathbb{C})$-Representations Distinguished by $\mathrm{GL}_n(\mathbb{R})$

This paper provides a complete classification of $\mathrm{GL}_n(\mathbb{R})$-distinguished irreducible representations of $\mathrm{GL}_n(\mathbb{C})$ when the representations are either generic or unitary. Additionally, for each such $\mathrm{GL}_n(\mathbb{R})$-distinguished representation, we explicitly construct the associated period and prove its non-vanishing on the distinguished minimal $K$-type. Furthermore, we offer some applications to the branching problem using theta correspondence.

math.RT↗
arXiv2024

Dirac series of U(n,2)

We determine the Dirac series of $U(n,2)$ and give related information about Dirac series: the spin lowest $K$-types are multiplicity free, and the Dirac cohomology are consistent with the Dirac index.

math.RT↗
arXiv2024

A resource-efficient variational quantum algorithm for mRNA codon optimization

Optimizing the mRNA codon has an essential impact on gene expression for a specific target protein. It is an NP-hard problem; thus, exact solutions to such optimization problems become computationally intractable for realistic problem sizes on both classical and quantum computers. However, approximate solutions via heuristics can substantially impact the application they enable. Quantum approximate optimization is an alternative computation paradigm promising for tackling such problems. Recently, there has been some research in quantum algorithms for bioinformatics, specifically for mRNA codon optimization. This research presents a denser way to encode codons for implementing mRNA codon optimization via the variational quantum eigensolver algorithms on a gate-based quantum computer. This reduces the qubit requirement by half compared to the existing quantum approach, thus allowing longer sequences to be executed on existing quantum processors. The performance of the proposed algorithm is evaluated by comparing its results to exact solutions, showing well-matching results.

quant-ph↗
arXiv2024

The unitary dual of $U(n,2)$

In this paper, we give a full classification of the unitary dual of $G = U(n,2)$ for $n \geq 3$. As a consequence, we determine which of these representations are weakly fair $A_{\mathfrak{q}}(\lambda)$-modules or special unipotent representations, resulting in a verification of a conjecture of Trapa and Vogan for $G$.

math.RT↗
arXiv2022

Dirac series of $\mathrm{GL}(n)$ over an Archimedean field

Motivated by the $(\mathfrak{g},K)$-cohomology and Dirac cohomology, we determine Dirac series of $\mathrm{GL}(n,\mathbb{H})$, and show that the spin lowest $K$-type of any Dirac series, which determines the Dirac cohomology, is unique and multiplicity-free for both $\mathrm{GL}(n,\mathbb{H})$ and $\mathrm{GL}(n,\mathbb{R})$. This verifies a conjecture about uniqueness of the spin lowest $K$-type of Dirac series for $\mathrm{GL}(n,\mathbb{R})$ proposed by Dong and Wong.

math.RT↗
arXiv2021

A generalization of Duflo's conjecture

In this article, we generalize Duflo's conjecture to understand the branching laws of non-discrete series. We give a unified description on the geometric side about the restriction of an irreducible unitary representation $π$ of $\mathrm{GL}_n(k)$, $k=\mathbb{R}$ or $\mathbb{C}$, to the mirabolic subgroup, where $π$ is attached to a certain kind of coadjoint orbit.

math.RT↗
arXiv2019

Evaluating bird collision risk of a high-speed railway crossing the habitat of the crested ibis (Nipponia nippon) in Qinling Mountains, China

Bird collisions with high-speed transport modes is a vital topic on vehicle safety and wildlife protection, especially when high-speed trains, with an average speed of 250km/h, have to run across the habitat of an endangered bird species. This paper evaluates the bird-train collision risk associated with a recent high-speed railway project in Qinling Mountains, China, for the crested ibis (Nipponia nippon) and other local bird species. Using line transect surveys and walking monitoring techniques, we surveyed the population abundance, spatial-temporal distributions, and bridge-crossing behaviors of the birds in the study area. The results show that: (1) The crested ibis and the egret were the two most abundant waterfowl species in the study area. The RAI of these two species were about 43.69% and 42.91%, respectively; (2) Crested ibises overall habitat closer to the railway bridge. 91.63% of them were firstly detected within the range of 0m to 25m of the vicinity of the bridge; (3) the ratio between crossing over and under the railway bridge was about 7:3. Crested ibises were found to prefer to fly over the railway bridge (89.29% of the total crossing activities observed for this species). Egrets were more likely to cross the railway below the bridge, and they accounted for 60.27% of the total observations of crossing under the bridge. We recommend that, while the collision risk of crested ibises could be low, barrier-like structures, such as fences, should still be considered to promote the conservation of multiple bird species in the area. This paper provides a practical case for railway ecology studies in China. To our best knowledge, this is the first high-speed railway project that takes protecting crested ibises as one of the top priorities, and exemplifies the recent nationwide initiative towards the construction of "eco-civilization" in the country.

q-bio.PE↗
arXiv2019

Designing wildlife crossing structures for ungulates in a desert landscape: A case study in China

This paper reports on the design of wildlife crossing structures (WCSs) along a new expressway in China, which exemplifies the country's increasing efforts on wildlife protection in infrastructure projects. The expert knowledge and field surveys were used to determine the target species in the study area and the quantity, locations, size, and type of the WCSs. The results on relative abundance index and encounter rate showed that the ibex (\textit{Capra ibex}), argali sheep (Ovis ammon), and goitered gazelle (Gazella subgutturosa) are the main ungulates in the study area. Among them, the goitered gazelle is the most widely distributed species. WCSs were proposed based on the estimated crossing hotspots. The mean deviation distance between those hotspots and their nearest proposed WCSs is around 341m. In addition, those 16 proposed underpass WCSs have a width of no less than 12m and height of no lower than 3.5m, which is believed to be sufficient for ungulates in the area. Given the limited availability of high-resolution movement data and wildlife-vehicle collision data during road's early design stage, the approach demonstrated in this paper facilitates practical spatial planning and provides insights into designing WCSs in a desert landscape.

q-bio.PE↗
arXiv2018

Carboxyl Carbon Quantum Dots: a Novel Type of Environmental-Friendly Scale Inhibitor

In this work, we demonstrate high inhibition efficiency of carboxyl carbon quantum dots (CCQDs) for the first time. The as-prepared CCQDs have excellent scale inhibition performance for calcium sulfate and barium sulfate. With static test of scale inhibition within temperature below 80 degrees, the anti-scaling efficiency can reach 100 % with low additions of CCQDs.

physics.app-ph↗