Related papers: A Hierarchical Array of Integrable Models

For a finite-dimensional Lie algebra $\mathfrak{L}$ over $\mathbb{C}$ with a fixed Levi decomposition $\mathfrak{L} = \mathfrak{g} \oplus \mathfrak{r}$ where $\mathfrak{g}$ is semi-simple, we investigate $\mathfrak{L}$-modules which…

We build a number of integrable one--scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose…

This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…

We introduce a new elliptic integrable $\sigma$-model in the form of a two-parameter deformation of the Principal Chiral Model on the group $\text{SL}_{\mathbb{R}}(N)$, generalising a construction of Cherednik for $N=2$ (up to reality…

We consider Grand Unified Theories in which the hierarchy between the unification and the Fermi scale emerges radiatively. Within the Pati-Salam framework, we show that it is possible to construct a viable model where the Higgs is an…

Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified…

The Randall-Sundrum model with the Higgs localized on the IR brane solves the gauge hierarchy problem. However, the associated low cutoff ($\Lambda \sim 10$ TeV) generically leads to unacceptably rapid nucleon decay and excessively large…

Let $F$ be a nonarchimedean local field with residue field of cardinality $q$, let $G$ be the $F$-points of a connected reductive group defined over $F$, let $P$ and $Q$ be two parabolic subgroups with the same Levi factor $M$. We construct…

We construct the ($\beta$-deformed) partition function hierarchies with $W$-representations. Based on the $W$-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur…

In Schubert Puzzles and Integrability I we proved several "puzzle rules" for computing products of Schubert classes in K-theory (and sometimes equivariant K-theory) of d-step flag varieties. The principal tool was "quantum integrability",…

Consider a hierarchical log-linear model, given by a simplicial complex, $\Gamma$, and integer matrix $A_\Gamma$. We give a new characterization of the rank of $A_\Gamma$ given by a logarithmic transformation on the exponential Hilbert…

A procedure is developed for constructing deformations of integrable sigma-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter sigma-model…

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…

This note gives a general construction of an integrable lattice model (and a solution of the Yang-Baxter equation with spectral parameter) from a four-dimensional field theory which is a mixture of topological and holomorphic. Spin-chain…

We construct a new class of integrable $\sigma$-models based on current algebra theories for a general semisimple group $G$ by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two…

This work hopes to be an introduction to Deligne categories for someone familiar with classical representation theory and some category theory. In the first chapter, we motivate and define (symmetric) tensor categories, construct the…

This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of…

A new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced. A fully analytical and general (i.e., valid for any lattice and set of weights) relationship between the autocorrelation…

We introduce the \emph{parameter-geometrization} to the Hitchin system, a paradigm embedding deformation parameters into geometry via the coupled Hitchin-He equations on a surface with boundary. A boundary term couples a second Higgs field…

In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type…