Related papers: Minimal presentations of gln-web categories
Webs are combinatorial diagrams used to encode homomorphisms between representations of Lie (super)algebras and related objects. This paper extends the theory of webs to the quantum group of type Q. We define a monoidal supercategory of…
We describe the underlying U_q(g)--module structure of representations of quantum affine algebras.
We give a generators and relations presentation for the full monoidal subcategory of representations of the quantum orthogonal group generated by the quantum exterior powers of the defining representation.
Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_2))$ is given. The full proof of the functional relations in the form…
We define and study representations of quantum toroidal $gl_n$ with natural bases labeled by plane partitions with various conditions. As an application, we give an explicit description of a family of highest weight representations of…
We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem,…
Explicit expressions for the generators of the quantum superalgebra $U_q[gl(n/m)]$ acting on a class of irreducible representations are given. The class under consideration consists of all essentially typical representations: for these a…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
In \cite{DFW} and \cite{Fu07}, little $q$-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups. In this paper, we will investigate representations of these algebras. We will classify simple modules for…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
This is an introduction to the quantum groups, or rather to the simplest quantum groups. The idea is that the unitary group $U_N$ has a free analogue $U_N^+$, whose standard coordinates $u_{ij}\in C(U_N^+)$ are allowed to be free, and the…
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…
These lectures present some basic facts in field theory necessary to understand the quantum theory of the Standard Model of weak and electromagnetic interactions.
A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_3))$ is given. The full proof of the functional relations in the form…
We construct a family of irreducible representations of the quantum continuous $gl_\infty$ whose characters coincide with the characters of representations in the minimal models of the $W_n$ algebras of $gl_n$ type. In particular, we obtain…
We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We give a diagrammatic presentation in terms of generators mod relations of the representation category of $U_q(\mathfrak{sl}_n)$. More precisely, we produce all the relations among $\rm{SL}_n$-webs, thus describing the full subcategory…