Related papers: Duality for generalized Gan-Gross-Prasad relevant …
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 prove a duality theorem for graded algebras over a field that implies several known duality results : graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and…
We quickly review the current status of gravitational duality in General Relativity. We summarize and comment some recent work on constructing dual (topological) charges and understanding how this duality acts in supergravity theories.
As basic variables in general relativity (GR) are chosen antisymmetric connection and bivectors - bilinear in tetrad area tensors subject to appropriate (bilinear) constraints. In canonical formalism we get theory with polinomial…
We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with its degree zero part and a graded module algebra for the…
In this paper, we start by defining a covering Barbasch-Vogan duality and prove some of its properties. Then, for genuine representations of $p$-adic covering groups we formulate an upper bound conjecture for their wavefront sets using this…
We determine the Ringel duals for all blocks in the parabolic versions of the BGG category O associated to a reductive finite dimensional Lie algebra. In particular we find that, contrary to the original category O and the specific…
Without using the $p$-adic Langlands correspondence, we prove that for many finite length smooth representations of $\mathrm{GL}_2(\mathbf{Q}_p)$ on $p$-torsion modules the $\mathrm{GL}_2(\mathbf{Q}_p)$-linear morphisms coincide with the…
Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G, we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized K\"ahler reduction exists even when only one generalized complex structure in the pair is preserved by the group…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
In this article, we establish the duality between the generalised Drinfeld double and generalised quantum codouble within the framework of modular or manageable (not necessarily regular) multiplicative unitaries, and discuss several…
In this paper we study the Gan-Gross-Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.
It is proved that generalized free product of two finite p-groups is a conjugacy p-separable group if and only if it is residually finite p-groups. This result is then applied to establish some sufficient conditions for conjugacy…
Let $G$ be a linear Lie group acting properly and isometrically on a $G$-spin$^c$ manifold $M$ with compact quotient. We show that Poincar\'e duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional…
Exchangeable sequences of random probability measures (partitions of mass) and their corresponding exchangeable bridges play an important role in a variety of areas in probability, statistics and related areas, including Bayesian…
We introduce and study the problem \mpd, which asks for two planar graphs $G_1$ and $G_2$ whether $G_1$ can be embedded such that its dual is isomorphic to $G_2$. Our algorithmic main result is an NP-completeness proof for the general case…
In this note the usual Goursat lemma, which describes subgroups of the direct product of two groups, is generalized to describing subgroups of a direct product $A_1\times A_2 \times...\times A_n$ of a finite number of groups. Other possible…
In this article, we construct bipartite graphs which are cospectral for both the adjacency and normalized Laplacian matrices using partitioned tensor product. This extends the construction of Ji, Gong, and Wang \cite{ji-gong-wang}. Our…