arXiv subjects
Publications and source records attributed to Hongmei Hu.
We investigate two families of central elements of the queer super Yangian ${\rm Y}(\mathfrak{q}_1)$, arising from the constructions of Poletaeva-Serganova and from Nazarov's quantum Berezinian. We establish an explicit relation between their generating series, thereby giving an answer to the question raised by Nazarov in \cite{Na22}.
We study the shuffle algebra realization of positive modular Yangians of classical type over an algebraically closed field of characteristic $p>3$. We show that, unlike in characteristic zero, the natural shuffle homomorphism has a nontrivial kernel. Its image is characterized by a $p$-wheel condition, while its kernel is precisely the ideal generated by the $p$-th powers of the Lyndon root vectors. This identifies the corresponding quotient with the small Yangian arising from a $\mathbb Z[\frac12]$-integral form. As part of the construction, we establish a PBW basis for the integral form and obtain the PBW theorem and $p$-center results for the Drinfeld presentation of modular Yangians.
We define the super Yangian $Y_{m|n}$ over a field $\mathbbm{k}$ of characteristic $2$, and show that the super Yangian $Y_{m|n}$ is a deformation of the super universal enveloping algebra of the current Lie algebra $\mathfrak{gl}_{m+n}[t]$. By employing the methods of the work of \cite{BT18}, we also give a description of the center of $Y_{m|n}$.
This paper aims to develop a grafting method to address Majid's conjecture. This method enables the construction of a larger target quantum group by grafting two given smaller quantum groups, and advances the study of the generation, classification, and construction of (quasi-)Hopf algebras. As a foundation for this construction, we establish a multi-tensor-product theory of generalized double-bosonization and use it to extract the crucial data for the associated braiding $R$-matrix. Beyond the braided monoidal category perspective arising from quantum subgroup representations, the grafting procedure needs to incorporate structural information from Lie-theoretic root systems. The resulting theoretic framework provides a one-stop strategy for resolving the generation problem concerning the quantum-groups tree in Majid's conjecture.
Personalized binaural audio reproduction is the basis of realistic spatial localization, sound externalization, and immersive listening, directly shaping user experience and listening effort. This survey reviews recent advances in deep learning for this task and organizes them by generation mechanism into two paradigms: explicit personalized filtering and end-to-end rendering. Explicit methods predict personalized head-related transfer functions (HRTFs) from sparse measurements, morphological features, or environmental cues, and then use them in the conventional rendering pipeline. End-to-end methods map source signals directly to binaural signals, aided by other inputs such as visual, textual, or parametric guidance, and they learn personalization within the model. We also summarize the field's main datasets and evaluation metrics to support fair and repeatable comparison. Finally, we conclude with a discussion of key applications enabled by these technologies, current technical limitations, and potential research directions for deep learning-based spatial audio systems.
We study the (extended) orthogonal Yangians associated to the Lie algebras types $B$ and $D$ over a field of positive characteristic. We define the $p$-center for the Yangians and obtain an explicit description of the center in terms of Drinfeld generators, showing that the center is generated by its Harish-Chandra center together with a large $p$-center.
We develop invariant theory for the quantum group ${\rm U}_q$ of $G_2$ at generic $q$ in the setting of braided symmetric algebras. Let ${\mathcal A}_m$ be the braided symmetric algebra over $m$-copies of the $7$-dimensional simple ${\rm U}_q$-module. A set of ${\rm U}_q$-invariants in ${\mathcal A}_m$ attached to certain acyclic trivalent graphs is obtained, which spans the subalgebra ${\mathcal A}_m^{{\rm U}_q}$ of invariants as vector space. A finite set of homogeneous elements is constructed explicitly, which generates ${\mathcal A}_m^{{\rm U}_q}$ as algebra. Commutation relations among the algebraic generators are determined. These results may be regarded as a non-commutative first fundamental theorem of invariant theory for ${\rm U}_q$. The algebra ${\mathcal A}_m$ is a non-flat quantisation of the coordinate ring of ${\mathbb C}^7\otimes{\mathbb C}^m$. As ${\rm U}_q$-module, ${\mathcal A}_m={\mathcal A}_1^{\otimes m}$ and we decompose ${\mathcal A}_1$ into simple submodules. The affine scheme associated to the classical limit of ${\mathcal A}_m$ is described. This is a rare case where the structure of a non-flat quantisation is understood.
The present paper is devoted to extend parabolic presentations, depending on an arbitrary composition of M+N and an arbitrary 01-sequence, of the super Yangian Y(M|N) to a field of positive characteristic.
This paper is devoted to the study of the shifted Yangian $Y_n(\sigma)$ associated to the general linear Lie algebra $\mathfrak{gl}_n$ over a field of positive characteristic. We obtain an explicit description of the center $Z(Y_n(\sigma))$ of $Y_n(\sigma)$ in terms of parabolic generators, showing that it is generated by its Harish-Chandra center and its $p$-center.
Given rising numbers of bilateral cochlear implant (CI) users, predominantly children, there is a clinical need for efficient and reliable tests that can objectively evaluate binaural hearing. These tests are crucial for guiding the setup of bilateral CIs to optimise delivery of binaural cues. Our primary goal is to introduce a clinical electroencephalogram (EEG) procedure to assess binaural hearing function at various stages within the auditory pathway. Previous research demonstrated that bilateral CI users significantly decrease in ability to discriminate interaural time differences when pulse rates exceed 300 pulses per second. Our paradigm utilizes different pulse rates to objectively explore the limits. A notable challenge with this EEG procedure is the interference induced by CI electrical stimulus artefacts. Despite this obstacle, the potential benefits of CI stimulation artefacts often go unnoticed. This paper outlines positive applications of the frequently criticized CI artefacts for optimizing the experiment setup.
Let $Y_{M|N}(\mathfrak{s})$ be the super Yangian associated with an arbitrary fixed $0^M1^N$-sequence $\mathfrak{s}$. In the present paper, we give a new formula for the quantum Berezinian by using the parabolic generators, which generalizes the usual expression in terms of RTT generators or Drinfeld generators.
Geometrical acoustics is well suited for simulating room reverberation in interactive real-time applications. While the image source model (ISM) is exceptionally fast, the restriction to specular reflections impacts its perceptual plausibility. To account for diffuse late reverberation, hybrid approaches have been proposed, e.g., using a feedback delay network (FDN) in combination with the ISM. Here, a computationally-efficient, digital-filter approach is suggested to account for effects of non-specular reflections in the ISM and to couple scattered sound into a diffuse reverberation model using a spatially rendered FDN. Depending on the scattering coefficient of a room boundary, energy of each image source is split into a specular and a scattered part which is added to the diffuse sound field. Temporal effects as observed for an infinite ideal diffuse (Lambertian) reflector are simulated using cascaded all-pass filters. Effects of scattering and multiple (inter-) reflections caused by larger geometric disturbances at walls and by objects in the room are accounted for in a highly simplified manner. Using a single parameter to quantify deviations from an empty shoebox room, each reflection is temporally smeared using cascaded all-pass filters. The proposed method was perceptually evaluated against dummy head recordings of real rooms.
The objective was to determine the effect of pulse rate on the sensitivity to use interaural-time-difference (ITD) cues and to explore the mechanisms behind rate-dependent degradation in ITD perception in bilateral cochlear implant (CI) listeners using CI simulations and electroencephalogram (EEG) measures. To eliminate the impact of CI stimulation artifacts and to develop protocols for the ongoing bilateral CI studies, upper-frequency limits for both behavior and EEG responses were obtained from normal hearing (NH) listeners using sinusoidal-amplitude-modulated (SAM) tones and filtered clicks with changes in either fine structure ITD or envelope ITD. Multiple EEG responses were recorded, including the subcortical auditory steady-state responses (ASSRs) and cortical auditory evoked potentials (CAEPs) elicited by stimuli onset, offset, and changes. Results indicated that acoustic change complex (ACC) responses elicited by envelope ITD changes were significantly smaller or absent compared to those elicited by fine structure ITD changes. The ACC morphologies evoked by fine structure ITD changes were similar to onset and offset CAEPs, although smaller than onset CAEPs, with the longest peak latencies for ACC responses and shortest for offset CAEPs. The study found that high-frequency stimuli clearly elicited subcortical ASSRs, but smaller than those evoked by lower carrier frequency SAM tones. The 40-Hz ASSRs decreased with increasing carrier frequencies. Filtered clicks elicited larger ASSRs compared to high-frequency SAM tones, with the order being 40-Hz-ASSR>160-Hz-ASSR>80-Hz-ASSR>320-Hz-ASSR for both stimulus types. Wavelet analysis revealed a clear interaction between detectable transient CAEPs and 40-Hz-ASSRs in the time-frequency domain for SAM tones with a low carrier frequency.
The present paper is devoted to studying the super Yangian $Y_{m|n}$ associated to the general linear Lie superalgebra $\mathfrak{gl}_{m|n}$ over a field of positive characteristic. We extend Drinfeld-type presentations of $Y_{m|n}$ and the special super Yangian $SY_{m|n}$ to positive characteristic. Moreover, the center $Z(Y_{m|n})$ of $Y_{m|n}$ is described: it is generated by its Harish-Chandra center together with a large $p$-center. We also study the $p$-center of $SY_{m|n}$ and provide another description of the $p$-center of $Y_{m|n}$ in terms of the RTT generators.
Double-bosonization construction in Majid \cite{majid1} is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \cite{HH1, HH2} have been depicted how to grow up. This paper continues to elucidate the type-crossing and inductive constructions of exceptional quantum groups of types $E_6$ and $E_7$, $E_8$, respectively, based on the generalized double-bosonization Theorem established in \cite{HH2}. Thus the Majid's expectation for the inductive constructions of $U_q(\mathfrak g)$'s for all finite-dimensional complex simple Lie algebras is completely achieved.
The purpose of the paper is to build up the related theory of weakly quasitriangular dual pairs suitably for non-standard $R$-matrices (irregular), and establish the generalized double-bosonization construction theorem for irregular $R$, which generalize Majid's results for regular $R$ in \cite{majid1}. As an application, the type-crossing construction for the exceptional quantum groups of types $F_{4}$, $G_{2}$ is obtained. This affirms the Majid's expectation that the tree structure of nodes diagram associated with quantum groups can be grown out of the node corresponding to $U_q(\mathfrak{sl}_2)$ by double-bosonization procedures. Notably from a representation perspective, we find an effective method to get the minimal polynomials for the non-standard $R$-matrices involved.
Both in Majid's double-bosonization theory and in Rosso's quantum shuffle theory, the rank-inductive and type-crossing construction for $U_q(\mathfrak g)$'s is still a remaining open question. In this paper, working with Majid's framework, based on our generalized double-bosonization Theorem proved in \cite{HH2}, we further describe explicitly the type-crossing construction of $U_q(\mathfrak g)$'s for $(BCD)_n$ series direct from type $A_{n-1}$ via adding a pair of dual braided groups determined by a pair of $(R, R')$-matrices of type $A$ derived from the respective suitably chosen representations. %which generalize the lower rank cases constructed in \cite{HH1}. Combining with our work in \cite{HH1,HH2,HH3}, this solves Majid's conjecture, that is, any quantum group $U_q(\mathfrak g)$ associated to a simple Lie algebra $\mathfrak g$ can be grown out of $U_q({\mathfrak {sl}}_2)$ inductively by a series of suitably chosen double-bosonization procedures.
Majid developed in \cite{majid3} his double-bosonization theory to construct $U_q(\mathfrak g)$ and expected to generate inductively not just a line but a tree of quantum groups starting from a node. In this paper, the authors confirm the Majid's first expectation (see p. 178 \cite{majid3}) through giving and verifying the full details of the inductive constructions of $U_q(\mathfrak g)$ for the classical types, i.e., the $ABCD$ series. Some examples in low ranks are given to elucidate that any quantum group of classical type can be constructed from the node corresponding to $U_{q}(\mathfrak{sl}_2)$.