Related papers: Level-Rank Duality in Kazama-Suzuki Models

We offer a classification of a broad and practically relevant class of symmetric double saddle-point system. At the core of the paper is the division of the associated matrices into ``block-arrow'' and ``block-tridiagonal'' forms. We…

We construct an integral model of the perfectoid modular curve. Studying this object, we prove some vanishing results for the coherent cohomology at perfectoid level. We use a local duality theorem at finite level to compute duals for the…

We prove the Avrunin-Scott theorem for quantum complete intersections; the rank variety of a module is isomorphic to its support variety.

We introduce (co)homology theory for multiple group racks and construct cocycle invariants of compact oriented surfaces in the 3-sphere using their 2-cocycles, where a multiple group rack is a rack consisting of a disjoint union of groups.…

We introduce a cup-cap duality in the Koszul calculus of N-homogeneous algebras. As an application, we prove that the graded symmetry of the Koszul cap product is a consequence of the graded commutativity of the Koszul cup product. We…

A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory…

We study global aspects of N=2 Kazama-Suzuki coset models by investigating topological G/H Kazama-Suzuki models in a Lagrangian framework based on gauged Wess-Zumino-Witten models. We first generalize Witten's analysis of the holomorphic…

Using the pure spinor formalism on the world-sheet, we derive the T-duality rules for all target space couplings in an efficient manner. The world-sheet path integral derivation is a proof of the equivalence of the T-dual Ramond-Ramond…

We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…

We propose a generalization of the level-rank dualities arising from Uglov's work on higher-level Fock spaces. The statements use Hecke algebras defined by Brou\'{e}-Malle, which conjecturally describe the endomorphisms of Lusztig induction…

We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant…

We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids.…

This paper is devoted to the proof of an isoperimetric property of the double spherical cap rearrangement of planar sets under the assumption of disconnection of non-trivial spherical slices. Additionally, the higher-dimensional case is…

In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co)homology are also mentioned.

We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss the implications of such construction at the level of Hodge…

The correspondence between two geometrical descriptions of the KP-hierarchy, one by discrete surface and another by difference analogue of differential geometry, is given.

We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface…

We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affine Schubert varieties. We apply this duality to…

We give an explicit construction of the Honda--Kazez--Mati\'c gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around, and to compute the trace in the sutured Floer…

We study a categorified generalization of Koszul duality that treats duality phenomena among monoidal categories. We establish Koszul duality results for stable monoidal infinity-categories associated with Artin algebras and related…