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

We prove a Cohen-Dimca-Orlik type theorem for rank one $\mathbb{Z}$-local systems on complex hyperplane arrangement complements. This settles a recent conjecture of S. Sugawara.

Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this…

We show that the multi-species higher spin stochastic vertex model, also called the U_q(A_n^{(1)}) vertex model, satisfies a duality where the indicator function has the form {\eta^x_{[1,n]} \geq \xi^x_{[1,n]} }. In other words, for every…

We review some recent results concerning Landau levels and Tomita-Takesaki modular theory. We also extend the general framework behind this to quasi *-algebras, to take into account the possible appearance of unbounded observables.

We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.

This paper provides an informal sketch of a proof of the Baez-Dolan cobordism hypothesis, which provides a classification for extended topological quantum field theories.

We consider some duality relations for models of non-interacting particles hopping on disordered one-dimensional chains. In particular, we discuss symmetries of bulk-driven barrier and trap models, and relations between boundary-driven and…

We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations intersect in the expected dimension. We also…

This is an extended abstract of our work "Level-Rank Dualities from $\Phi$-Cuspidal Pairs..." We present evidence for a family of surprising coincidences within the representation theory of a finite reductive group $G$: more precisely,…

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…

We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…

We use topological K-theory to study non-singular varieties with quadratic entry locus. We thus obtain a new proof of Russo's Divisibility Property for locally quadratic entry locus manifolds. In particular we obtain a K-theoretic proof of…

In this work we develop some categorical aspects of the double structure of a module.

We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and for some fixed parameter value of the system.…

In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level…

We investigate the possible classification of zero-temperature spin-gapped phases of multicomponent electronic systems in one spatial dimension. At the heart of our analysis is the existence of non-perturbative duality symmetries which…

Let $Z'\subset \mathbb{P}^{n}$ be a smooth projective hypersurface of degree $d>1$ and let $Z\to \mathbb{P}^n$ be the $\mu_d$-cover totally ramified along $Z'$. We relate full level $d$ structures on the primitive cohomology $Z'$ with full…

A duality of $\kappa$-normed topological vector spaces is defined and investigated. For such spaces the analog of the Mackey-Arens theorem is proved. There are investigated cases, when $\kappa$-normability of a topological vector space…

We construct labeling homomorphisms on the cubical homology of higher-dimensional automata and show that they are natural with respect to cubical dimaps and compatible with the tensor product of HDAs. We also indicate two possible…

We give a new proof of a result of Lazarev, that the dual of the circle $S^1_+$ in the category of spectra is equivalent to a strictly square-zero extension as an associative ring spectrum. As an application, we calculate the topological…