Dualities and reciprocities on graphs on surfaces

In this paper, we extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally bi-walkable orientations. In addition, we provide a reciprocity theorem connecting local tensions and boundary acyclic orientations. Furthermore, we define balanced flow polynomial which is connected with tension polynomial by duality and with totally bi-walkable orientations by reciprocity.Comment: 14 pages, 7 figures, comments welcome

Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras

We introduce a new family of superalgebras $\overrightarrow{B}_{r,s}$ for $r, s \ge 0$ such that $r+s>0$, which we call the walled Brauer superalgebras, and prove the mixed Scur-Weyl-Sergeev duality for queer Lie superalgebras. More precisely, let $\mathfrak{q}(n)$ be the queer Lie superalgebra, ${\mathbf V} =\mathbb{C}^{n|n}$ the natural representation of $\mathfrak{q}(n)$ and ${\mathbf W}$ the dual of ${\mathbf V}$. We prove that, if $n \ge r+s$, the superalgebra $\overrightarrow{B}_{r,s}$ is isomorphic to the supercentralizer algebra _{\mathfrak{q}(n)}({\mathbf V}^{\otimes r} \otimes {\mathbf W}^{\otimes s})^{\op} of the $\mathfrak{q}(n)$-action on the mixed tensor space ${\mathbf V}^{\otimes r} \otimes {\mathbf W}^{\otimes s}$. As an ingredient for the proof of our main result, we construct a new diagrammatic realization $\overrightarrow{D}_{k}$ of the Sergeev superalgebra $Ser_{k}$. Finally, we give a presentation of $\overrightarrow{B}_{r,s}$ in terms of generators and relations

Slave rotor theory of antiferromagnetic Hubbard model

The slave-rotor mean-field theory of Florens and Georges is generalized to the antiferromagnetic phase of the Hubbard model. An effective action consisting of a spin rotor and a fermion is derived and the corresponding saddle-point action is analyzed. Zero-temperature phase diagram of the antiferromagnetic Hubbard model is presented. While the magnetic phase persists for all values of the Hubbard interaction U, the single-particle spectral function exhibits a crossover into an incoherent phase when the magnetic moment m (and the corresponding U values) lies within a certain window m_c < m < 1-m_c, indicating a possible deviation from the Hartree-Fock theory

Quantum queer superalgebras

We give a brief survey of recent developments in the highest weight representation theory and the crystal basis theory of the quantum queer superalgebra $U_q(\mathfrak{q}(n))$.Comment: For proceedings of "Representation Theory of Algebraic Groups and Quantum Groups," Nagoya, 201

Boltzmann-equation approach to anomalous transport in a Weyl metal

Weyl metal is regarded as a platform toward interacting topological states of matter, where its topological structure gives rise to anomalous transport phenomena, referred to as chiral magnetic effect and "negative" magneto-resistivity, the origin of which is chiral anomaly. Recently, the negative magneto-resistivity has been observed with the signature of weak anti-localization at $x = 3 \sim 4 ~ \%$ in Bi$_{1-x}$Sb$_{x}$, where magnetic field is applied in parallel with electric field. Based on the Boltzmann-equation approach, we find the negative magneto-resistivity in the presence of weak anti-localization. An essential ingredient is to introduce the topological structure of chiral anomaly into the Boltzmann-equation approach, resorting to semi-classical equations of motion with Berry curvature

Admissible Pictures and Uq(gl(m,n))U_q(gl(m,n))-Littlewood-Richardson Tableaux

We construct a natural bijection between the set of admissible pictures and the set of $U_q(gl(m,n))$-Littlewood-Richardson tableaux.Comment: 13page

A categorification of q(2)\mathfrak{q}(2)-crystals

We provide a categorification of $\mathfrak{q}(2)$-crystals on the singular $\mathfrak{gl}_{n}$-category ${\mathcal O}_{n}$. Our result extends the $\mathfrak{gl}_{2}$-crystal structure on ${\rm Irr} ({\mathcal O}_{n})$ defined by Bernstein-Frenkel-Khovanov. Further properties of the ${\mathfrak q}(2)$-crystal ${\rm Irr}({\mathcal O}_{n})$ are also discussed.Comment: 20 pages, minor changes are made in v.2, Remark 2.3 is inserted with minor corrections in v.3, to appear in Algebras and Representation Theor

An iALM-ICA-based Anti-Jamming DS-CDMA Receiver for LMS Systems

We consider a land mobile satellite communication system using spread spectrum techniques where the uplink is exposed to MT jamming attacks, and the downlink is corrupted by multi-path fading channels. We proposes an anti-jamming receiver, which exploits inherent low-dimensionality of the received signal model, by formulating a robust principal component analysis (Robust PCA)-based recovery problem. Simulation results verify that the proposed receiver outperforms the conventional receiver for a reasonable rank of the jamming signal.Comment: IEEE Transactions on Aerospace and Electric Systems, "accepted

Quantum Queer Superalgebra and Crystal Bases

In this paper, we develop the crystal basis theory for the quantum queer superalgebra \Uq. We define the notion of crystal bases, describe the tensor product rule, and present the existence and uniqueness of crystal bases for finite-dimensional \Uq-modules in the category $\mathcal{O}_{int}^{\ge 0}$.Comment: 11pages, 3 figure

Crystal bases for the quantum queer superalgebra

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak q(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak q(n))$-modules in the category $O_int^{\geq 0}$. Our main theorem shows that every $U_q(\mathfrak q(n))$-module in the category $O_int^{\geq 0}$ has a unique crystal basis.Comment: 38 pages, small changes on acknowledgemen