Related papers: Unitary dual of quasi-split $PGSO_8^E$
Analogues of JSJ decompositions were developed for Poincar\'e duality pairs in [19]. These decompositions depend only on the group. Our focus will be on describing the edge splittings of these decompositions more precisely. We use our…
This paper is a coalgebra version of arXiv:1703.04266 and a sequel to arXiv:1607.03066. We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras $\mathcal C$ and $\mathcal D$. For any…
We show how in PT-symmetric 2J-level quantum systems the assumption of an upside-down symmetry (or duality) of their spectra simplifies their classification based on the non-equivalent pairwise mergers of the energy levels.
In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them…
In this note we settle some technical questions concerning finite rank quasi-free Hilbert modules and develop some useful machinery. In particular, we provide a method for determining when two such modules are unitarily equivalent. Along…
In this paper, we classify irreducible representations of affine group superschemes over fields $F$ of characteristic not two in terms of those over a separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute the…
This paper surveys what is known about (conjectural) $p$-adic and $p$-modular semisimple Langlands correspondences in the non-supercuspidal setting for the unramified quasi-split unitary group…
A class of integrable boundary terms for the eight-state supersymmtric $U$ model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz…
We initiate the study of a new notion of duality defined with respect to the module Haagerup tensor product. This notion not only recovers the standard operator space dual for Hilbert $C^*$-modules, it also captures quantum group duality in…
For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the…
The doublet-triplet splitting problem in supersymmetric grand unified theories is elegantly solved in a supersymmetric SO(10)_GUT x SO(6)_H model. In this model, the gauginos in the supersymmetric standard model do not respect the usual GUT…
In our previous paper, we gave a complete classification of the unitary highest weight modules for the universal covers of the Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$, using the Dirac inequality and the so called PRV…
Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…
In this paper, we obtain a full classification of reductive dual pairs in a, real or complex, Lie superalgebra $\mathfrak{spo}(E)$ and Lie supergroup $\textbf{SpO}(E)$. Moreover, by looking at the natural action of the orthosymplectic Lie…
Let $\R$ be a real closed field, $ {\mathcal Q} \subset \R[Y_1,...,Y_\ell,X_1,...,X_k], $ with $ \deg_{Y}(Q) \leq 2, \deg_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m,$ and $ {\mathcal P} \subset \R[X_1,...,X_k] $ with $\deg_{X}(P)…
Let $ E \xrightarrow[\text{}]{\pi} B$ be an oriented circle bundle over an oriented closed surface $B$. A quasisection is a smooth surface ${Q}$ (either closed or bordered) mapped by a generic smooth mapping $q$ to $E$ such that $\pi\circ…
We introduce a tensor decomposition of the $\ell$-adic Tate module of an abelian variety $A_0$ defined over a number field which is geometrically isotypic. If $A_0$ is potentially of $\GL_2$-type and defined over a totally real number…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…
Okamoto has obtained a sequence of $\tau$-functions for the \PVI system expressed as a double Wronskian determinant based on a solution of the Gauss hypergeometric equation. Starting with integral solutions of the Gauss hypergeometric…
In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the…