Related papers: Multiparameter quantum Pfaffians
We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among the quantum determinant, Sklyanin determinants associated…
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well…
We introduce uniparametric and multiparametric quantisations of the general linear supergroup, in the form of "quantised function algebras", both in a formal setting - yielding "quantum formal series Hopf superalgebras", a` la Drinfeld -…
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
We introduce a multiparametric quantum superspace with $m$ even generators and $n$ odd generators whose commutation relations are in the sense of Manin such that the corresponding algebra has a Hopf superalgebra. By using its Hopf…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
For any homogeneous identity between $q$-minors, we provide an identity between $P,Q$-minors.
We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use of modified characteristic identity methods and…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We establish a criterion for the classical…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. Operators of differentiation with respect to paragrassmann variables and a covariant…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
For the two-parameter matrix quantum group GLp,q(2) all bicovariant differential calculi (with a four-dimensional space of 1-forms) are known. They form a one-parameter family. Here, we give an improved presentation of previous results by…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.