Related papers: Webs for the Quantum Orthogonal Group
We study unitarity of the induced representations from coisotropic quantum subgroups which were introduced in math.QA/9804138. We define a real structure on coisotropic subgroups which determines an involution on the homogeneous space. We…
In this paper we prove some general theorems about representations of finite groups arising from the inner semidirect product of groups. We show how these results can be used for standard applications of group theory in quantum chemistry…
A short description is given of a construction of representations for quantum groups. The method uses infinitesimal dressing transformation on quantum homogeneous spaces and is illustrated on an example of Uq(so(5)).
The extension of FRT quantization theory for the nonsemisimple CK groups is suggested. The quantum orthogonal CK groups are realized as the Hopf algebras of the noncommutative functions over an associative algebras with nilpotent…
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…
We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.
The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength…
We provide an alternative approach to the Faddeev-Reshetikhin-Takhtajan presentation of the quantum group U_q(g), with L-operators as generators and relations ruled by an R-matrix. We look at U_q(g) as being generated by the quantum Borel…
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
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…
The orthogonal group acts on the space of several $n\times n$ matrices by simultaneous conjugation. For an infinite field of characteristic different from two, relations between generators for the algebra of invariants are described. As an…
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.
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
We construct super-version of Quantum Representation Theory. The quadratic super-algebras and operations on them are described. We also describe some important monoidal functors. We proved that the monoidal category of graded super-algebras…
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.
Let group generators having finite-dimensional representation be realized as Hermitian linear differential operators without nhomogeneous terms as takes place, for example, for the SO(n) group. Then orresponding group Hamiltonians…
We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…