Related papers: SPINON BASIS FOR (sl2^)_k INTEGRABLE HIGHEST WEIGH…

The basis of spinors in three-dimensional Euclidean space is expressed by differential forms. Its expression is found from the spectral decomposition of the modified Hamiltonian describing Weyl semimetals where the wavenumber parameters are…

In this paper we study special bases of certain spaces of half-integral weight weakly holomorphic modular forms. We establish a criterion for the integrality of Fourier coefficients of such bases. By using recursive relations between Hecke…

Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…

In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin $R$-matrix is associated with the affine quantum algebra $U_q(\widehat{sl(2)})$. The…

Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a…

We present complete realization of irreducible $A_1 ^{(1)}$-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal…

We provide quantitative weighted estimates for the $L^p(w)$ norm of a maximal operator associated to cube skeletons in $\mathbb{R}^n$. The method of proof differs from the usual in the area of weighted inequalities since there are no…

Let $\tilde{\mathfrak{g}}$ be the affine Lie algebra of type $A_{2l}^{(2)}$. The integrable highest weight $\tilde{\mathfrak{g}}$-module $L(k\Lambda_0)$ called the standard $\tilde{\mathfrak{g}}$-module is realized by a tensor product of…

Let $p>2$ be a prime. Let $K$ be a tamely ramified finite extension over $\mathbb Q_p$ with ramification index $e$, and let $G_K$ be the Galois group. We study Kisin modules attached to crystalline representations of $G_K$ whose labeled…

We formulate a theory of invariants for the spin symmetric group in some suitable modules which involve the polynomial and exterior algebras. We solve the corresponding graded multiplicity problem in terms of specializations of the Schur…

We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $\mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all…

A representation of the Quantum Toroidal Algebra of type sl(N) is constructed on every irreducible integrable highest weight module of the Quantum Affine Algebra of type gl(N). As an intermediate step in the construction, we obtain a…

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model.…

In this study, an integrable vertex model based on the quantum affine superalgebra $U_q\bigl(\hat{gl}(2|2)\bigr)$ is constructed. The model is characterized by a particular assignment of spectral parameters and lowest as well as highest…

Let $\tilde{\mathfrak g}$ be an affine Lie algebra of type $A_\ell^{(1)}$. Suppose we're given a $\mathbb Z$-gradation of the corresponding simple finite-dimensional Lie algebra ${\mathfrak g}={\mathfrak g}_{-1}\oplus{\mathfrak g}_0 \oplus…

Let $\mathfrak{g}$ be a complex simple Lie algebra and $L(\lambda)$ be a highest weight module of $\mathfrak{g}$ with highest weight $\lambda-\rho$, where $\rho$ is half the sum of positive roots. A simple $\mathfrak{g}$-module…

Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$, we establish an equivalence between parabolic BGG categories of a Kac-Moody Lie superalgebra and a Kac-Moody Lie algebra. The characters for a…

We study certain subspaces of solutions to the sl_2 rational qKZ equation at level zero. Each subspace is specified by the vanishing of the residue at a certain divisor which stems from models in two dimensional integrable field theories.…

We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody…

This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special linear groups of 2 by 2 matrices. Let R be a…