Related papers: Highest Weight Generating Functions for Hilbert Se…

This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equations. We propose a new combination of an Adaptive Wavelet…

The purpose of this note is to define and construct highest weight modules for Felder's elliptic quantum groups. This is done by using exchange matrices for intertwining operators between (not necessarily finite-dimensional) modules over…

The $SU_{q}(n)$ generators are obtained as large spectral parameter limit of the Yang-Baxter operators in the integrable $SU_{q}(n)$ invariant vertex model. The commutation relations, including Serre relations, are obtained as limits of the…

In this article, we study weighted estimates for a general class of lacunary maximal functions on homogeneous groups. As an application we derive improved weighted estimates for the lacunary maximal function associated to the Kor\'anyi…

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on…

Assuming the Riemann hypothesis for $L$-functions attached to primitive Dirichlet characters, modular cusp forms, and their tensor products and symmetric squares, we write down explicit finite sets of Hecke operators that span the Hecke…

The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that…

Following the method of induced group representations of Wigner-Mackay, the explicit construction of all the unitary irreducible representations of the discrete finite Heisenberg-Weyl group $HW_{2^s}$ over the discrete phase space lattice…

Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of polynomial functions on…

We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by…

In this work we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the $L^2$ product in each cell of the discretization, we are able to…

Making use of a Howe duality involving the infinite-dimensional Lie superalgebra $\hgltwo$ and the finite-dimensional group $GL_l$ we derive a character formula for a certain class of irreducible quasi-finite representations of $\hgltwo$ in…

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra U_{q,p}(\hat{sl}_2). The algebra U_{q,p}(\hat{sl}_2) has a constructive definition in terms of the…

We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten…

In [19], Zheng studied the bounded derived categories of constructible $\bar{\mathbb{Q}}_l$-sheaves on some algebraic stacks consisting of the representations of a enlarged quiver and categorified the integrable highest weight modules of…

The properties of highest-weight representations of the N=2 superconformal algebra in two dimensions can be considerably simplified when re-expressed in terms of relaxed ^sl(2) representations. This applies to the appearance of submodules…

In this paper we study the characters of sequences of representations of any of the three families of classical Weyl groups W_n: the symmetric groups, the signed permutation groups (hyperoctahedral groups), or the even-signed permutation…

In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this…

A holographic model of chiral symmetry breaking is used to study the dynamics plus the meson and baryon spectrum of the underlying strong dynamics in composite Higgs models. The model is inspired by top-down D-brane constructions. We…