Related papers: Mirabolic Howe duality
Duality is considered for the perturbation theory by deriving, given a series solution in a small parameter, its dual series with the development parameter being the inverse of the other. A dual symmetry in perturbation theory is…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
In this paper, we carry out the ``quantum double construction'' of the specific quantum groups we constructed earlier, namely, the ``quantum Heisenberg group algebra'' (A,\Delta) and its dual, the ``quantum Heisenberg group''…
We establish algebraically and geometrically a duality between the Iwahori-Hecke algebra of type D and two new quantum algebras arising from the geometry of N-step isotropic flag varieties of type D. This duality is a type D counterpart of…
We generalise the quantum double construction of Drinfel'd to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the *-algebra structure of the quantum double. If the conjugacy…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
We develop an invariant theory of quasi-split $\imath$quantum groups $\mathbf{U}_n^\imath$ of type AIII on a tensor space associated to $\imath$Howe dualities. The first and second fundamental theorems for $\mathbf{U}_n^\imath$-invariants…
Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be…
Let $ G^\tau $ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfel'd structure of Poisson group, let $ H^\tau $ be its dual Poisson group. By means of quantum double construction and…
It is proposed that the physical universe is an instance of a mathematical structure which possesses a dual structure, and that this dual structure is the collection of all possible knowledge of the physical universe. In turn, the physical…
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian…
We establish a version of Howe duality that involves a tensor product of Verma modules. Surprisingly, this duality leaves the realm of lowest and highest weight modules. We quantize this duality, and as an application, we prove that the…
We obtain two related characterizations of discrete quantum groups and discrete quantum groups of Kac type as allegorical group objects in the symmetric monoidal dagger category of quantum sets and relations, of interest to quantum…
The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are…
We describe types of double magma associated with Ward quasigroups, double Ward quasigroups, their duals and the groups they generate. Ward quasigroup double magma and unipotent, right modular, left unital double magma are proved to be…
We establish a Schur-Weyl duality between a shifted quantum affine algebra and an Ariki-Koike algebra. Then, we realize a cyclotomic $q$-Schur algebra in the context of the Schur-Weyl duality.
We explain how Lie superalgebras of types gl and osp provide a natural framework generalizing the classical Schur and Howe dualities. This exposition includes a discussion of super duality, which connects the parabolic categories O between…
Two descriptions of the dual $-1$ Hahn algebra are presented and shown to be related under Howe duality. The dual pair involved is formed by the Lie algebra $\mathfrak{o}(4)$ and the Lie superalgebra $\mathfrak{osp}(1|2)$.