Related papers: Embeddings among quantum affine $\mathfrak{sl}_n$

A level-one representation of the quantum affine superalgebra $\U_q(\hat{\frak{sl}}(M+1|N+1))$ and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields. Character formulas of…

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…

We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by…

Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find…

In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations…

We study Lusztig's theory of cells for quantum affine $\mathfrak{sl}_n$. Using the geometric construction of the quantum group due to Lusztig and Ginzburg--Vasserot, we describe explicitly the two-sided cells, the number of left cells in a…

In this paper, by using Gr\"obner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative…

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…

We complete the classification of conformal embeddings of a maximally reductive subalgebra $\mathfrak k$ into a simple Lie algebra $\mathfrak g$ at non-integrable non-critical levels $k$ by dealing with the case when $\mathfrak k$ has rank…

We obtain a presentation of quantum Schur algebras (over the field Q(v)) by generators and relations. This presentation is compatible with the usual presentation of the quantized universal enveloping algebra of the Lie algebra gl(2). We…

By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is…

Knowledge graph embedding has recently become a popular way to model relations and infer missing links. In this paper, we present a group theoretical perspective of knowledge graph embedding, connecting previous methods with different group…

We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes…

By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary $sl_2$ embeddings we show that a large set $\cal W$ of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set $\cal W$ contains…

Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.

Concept embeddings offer a practical and efficient mechanism for injecting commonsense knowledge into downstream tasks. Their core purpose is often not to predict the commonsense properties of concepts themselves, but rather to identify…

In 1990, Beilinson-Lusztig-MacPherson (BLM) discovered a realization \cite[5.7]{BLM} for quantum $\frak{gl}_n$ via a geometric setting of quantum Schur algebras. We will generailze their result to the classical affine case. More precisely,…

Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems…

It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in…

For an algebraically closed field $k$ of characteristic zero and a linear algebraic $k$-group $G$, it is well known that every affine $G$-variety admits a $G$-equivariant closed embedding into a finite-dimensional $G$-module. Such an…