Related papers: On highest weight modules over elliptic quantum gr…
Consider the affine Lie algebra $\hat{s\ell}(n)$ with null root $\delta$, weight lattice $P$ and set of dominant weights $P^+$. Let $V(k\Lambda_0), \, k \in \mathbb{Z}_{\geq 1}$ denote the integrable highest weight $\hat{s\ell}(n)$-module…
We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.
In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
Let $\mathfrak{g}=\mathfrak{g}_{\bar0}+\mathfrak{g}_{\bar1}$ be a basic classical Lie superalgebra over $\mathbb{C}$, and $e=e_{\theta}\in\mathfrak{g}_{\bar0}$ with $-\theta$ being a minimal root of $\mathfrak{g}$. Set $U(\mathfrak{g},e)$…
The aim of this paper is to evaluate in terms of q-special functions the objects (intertwining map, fusion matrix, exchange matrix) related to the quantum dynamical Yang-Baxter equation (QDYBE) for infinite dimensional representations…
Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its…
The main purpose of this paper is computing higher algebraic $K$-theory of Koszul complexes over principal ideal domains. The second purpose of this paper is giving examples of comparison techniques on algebraic $K$-theory for Waldhausen…
We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras $\hgltwo$, $\hC$ and $\hD$, and determine the necessary and sufficient conditions for quasi-finite irreducible highest weight modules…
We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consisting of free modules with edges being classical matrix…
The affine evaluation map is a surjective homomorphism from the quantum toroidal ${\mathfrak {gl}}_n$ algebra ${\mathcal E}'_n(q_1,q_2,q_3)$ to the quantum affine algebra $U'_q\widehat{\mathfrak {gl}}_n$ at level $\kappa$ completed with…
We give a path model for a level zero extremal weight module over a quantum affine algebra. By using this result, we prove a branching rule for an extremal weight module with respect to a Levi subalgebra. Furthermore, we also show a…
In this paper, we propose a conjectural formula for the highest $\ell$-weight monomial of an arbitrary real module over a simply-laced quantum affine algebra. We verify the conjecture under a multiplicative reachability condition, answering…
The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Similarly, explicit closed formulas for the multiplicities of…
This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space $W$,…
We study canonical basis elements in higher-level Fock spaces associated with the quantum group $U_q(\mathfrak{gl}_\infty)$, which are conjecturally related to Calogero-Moser theory for complex reflection groups. We generalize the…
Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$ having rank $l$ and let $V=L(\lambda)$ be an irreducible finite-dimensional $\mathfrak{g}$-module having highest weight $\lambda.$ Computations of weight multiplicities in…
In the present paper, using the technique of localization, we determine the center of the quantum Schr\"{o}dinger algebra $\S_q$ and classify simple modules with finite-dimensional weight spaces over $\S_q$, when $q$ is not a root of unity.…
The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.
In this article we present an algorithm that uses the graded algebra structure of Hilbert modular forms to compute the adelic $q$-expansion of Hilbert modular forms of weight one as the quotient of Hilbert modular forms of higher weight.…