Two-boundary centralizer algebras for q(n)

We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the natural module for $\mathfrak{q}(n)$, and $M, N$ are arbitrary modules for $\mathfrak{q}(n)$, the Lie superalgebra of Type Q. When $M$ and $N$ are irreducible highest weight modules parametrized by a staircase partition and a single row, respectively, this action factors through a quotient of $\mathcal{H}_d$. Our second goal is to directly construct modules for this quotient, $\mathcal{H}^p_d$, using combinatorial tools such as shifted tableaux and the Bratteli graph. These modules belong to a family of modules which we call calibrated. Using the relations in $\mathcal{H}^p_d$, we also classifiy a specific class of calibrated modules. This result provides connection to a Schur-Weyl type duality: the irreducible summands of $M\otimes N\otimes V^{\otimes d}$ coincide with the combinatorial construction

SL2 tilting modules in the mixed case

Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for $\mathrm{SL}_{2}$ in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the appropriate analog of Jones-Wenzl projectors. We also discuss certain theta values, the tensor ideals, mixed Verlinde quotients and the non-degeneracy of the braiding.Comment: 53 pages, many figures, comments welcom

McKay Matrices for Finite-dimensional Hopf Algebras

For a finite-dimensional Hopf algebra $A$, the McKay matrix $M_V$ of an $A$-module $V$ encodes the relations for tensoring the simple $A$-modules with $V$. We prove results about the eigenvalues and the right and left (generalized) eigenvectors of $M_V$ by relating them to characters. We show how the projective McKay matrix $Q_V$ obtained by tensoring the projective indecomposable modules of $A$ with $V$ is related to the McKay matrix of the dual module of $V$. We illustrate these results for the Drinfeld double $D_n$ of the Taft algebra by deriving expressions for the eigenvalues and eigenvectors of $M_V$ and $Q_V$ in terms of several kinds of Chebyshev polynomials. For the matrix $N_V$ that encodes the fusion rules for tensoring $V$ with a basis of projective indecomposable $D_n$-modules for the image of the Cartan map, we show that the eigenvalues and eigenvectors also have such Chebyshev expressions.Comment: 41 pages, minor changes according to the referees' suggestions, the appendix is removed from version

Tensor Representations for the Drinfeld Double of the Taft Algebra

For the Drinfeld double $D_n$ of the Taft algebra $A_n$ defined over an algebraically closed field $\mathbb k$ of characteristic zero using a primitive $n$th root of unity $q \in \mathbb k$ for $n$ odd, $n\ge3$, we determine the ribbon element of $D_n$ explicitly. We use the R-matrix and ribbon element of $D_n$ to construct an action of the Temperley-Lieb algebra $\mathsf{TL}_k(\xi)$ with $\xi = -(q^{\frac{1}{2}}+q^{-\frac{1}{2}})$ on the $k$-fold tensor power of any two-dimensional simple $D_n$-module. When the two-dimensional module is the unique self-dual simple module $V$, we develop a diagrammatic algorithm for computing the $\mathsf{TL}_k(\xi)$-action. We show that this action on $V^{\otimes k}$ is faithful for arbitrary $k \ge 1$ and that $\mathsf{TL}_k(\xi)$ is isomorphic to the centralizer algebra $\text{End}_{D_n}(V^{\otimes k})$ for $1 \le k\le 2n-2$.Comment: 37 pages with minor wording changes. The appendix is removed from the first version to shorten the pape

The COVID-19 pandemic and Bitcoin: Perspective from investor attention

The response of the Bitcoin market to the novel coronavirus (COVID-19) pandemic is an example of how a global public health crisis can cause drastic market adjustments or even a market crash. Investor attention on the COVID-19 pandemic is likely to play an important role in this response. Focusing on the Bitcoin futures market, this paper aims to investigate whether pandemic attention can explain and forecast the returns and volatility of Bitcoin futures. Using the daily Google search volume index for the “coronavirus” keyword from January 2020 to February 2022 to represent pandemic attention, this paper implements the Granger causality test, Vector Autoregression (VAR) analysis, and several linear effects analyses. The findings suggest that pandemic attention is a granger cause of Bitcoin returns and volatility. It appears that an increase in pandemic attention results in lower returns and excessive volatility in the Bitcoin futures market, even after taking into account the interactive effects and the influence of controlling other financial markets. In addition, this paper carries out the out-of-sample forecasts and finds that the predictive models with pandemic attention do improve the out-of-sample forecast performance, which is enhanced in the prediction of Bitcoin returns while diminished in the prediction of Bitcoin volatility as the forecast horizon is extended. Finally, the predictive models including pandemic attention can generate significant economic benefits by constructing portfolios among Bitcoin futures and risk-free assets. All the results demonstrate that pandemic attention plays an important and non-negligible role in the Bitcoin futures market. This paper can provide enlightens for subsequent research on Bitcoin based on investor attention sparked by public emergencies

Anomalous stopping of laser-accelerated intense proton beam in dense ionized matter

Ultrahigh-intensity lasers (10$^{18}$-10$^{22}$W/cm$^{2}$) have opened up new perspectives in many fields of research and application [1-5]. By irradiating a thin foil, an ultrahigh accelerating field (10$^{12}$ V/m) can be formed and multi-MeV ions with unprecedentedly high intensity (10$^{10}$A/cm$^2$) in short time scale ($\sim$ps) are produced [6-14]. Such beams provide new options in radiography [15], high-yield neutron sources [16], high-energy-density-matter generation [17], and ion fast ignition [18,19]. An accurate understanding of the nonlinear behavior of beam transport in matter is crucial for all these applications. We report here the first experimental evidence of anomalous stopping of a laser-generated high-current proton beam in well-characterized dense ionized matter. The observed stopping power is one order of magnitude higher than single-particle slowing-down theory predictions. We attribute this phenomenon to collective effects where the intense beam drives an decelerating electric field approaching 1GV/m in the dense ionized matter. This finding will have considerable impact on the future path to inertial fusion energy.Comment: 8 pages, 4 figure