Related papers: Quantum diagrammatics for $F_4$
In this talk we review the classification of the irreducible representations of the algebra of the N-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060,…
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
This work is motivated to study the representation theory of the non-semisimple deformed Fomin-Kirillov algebras $\mathcal{D}_4(\alpha_1, \alpha_2)$. In particular, we consider Gabriel's theorem applications in regard of constructing…
Representation theory, for the classical binary polyhedral groups is encoded by the affine Dynkin diagrams E6^{(1)}, E7^{(1)} and E8^{(1)} (McKay correspondance). The quantum versions of these classical geometries are associated with…
We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…
We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of…
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
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…
The tensor categories of oriented Kauffman diagrams are studied with description of fiber functors on them as well as the associated Hopf algebras.
The coadjoint orbits for the series $B_l,\ C_l$ and $D_l$ are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a $\ast$-algebra generated…
We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.
In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These perturbative quantum geometries determine the number contents of the amplitude considered. In the article `Modular forms in…
We present a new model of quantum computation rooted in the representation theory of the mass less sector of unitary irreducible representations of the extended Poincare group developed in [1].
In this paper we define a quantum version of the ``fusion'' tensor product of two representations of an affine Kac-Moody algebra.It is replaced by what we call fusion action of the category of finite-dimensional representations of quantum…
We provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of $\mathfrak{sl}_2$ at a root of unity $q$ of odd order. Our approach is diagrammatic, and it relies on…
Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces to construct a certain positive-dimensional family of irreducible…
We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a homogeneous rooted tree.