Related papers: A field of quantum upper triangular matrices
After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a…
The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are…
Explicit construction of the second order left differential calculi on the quantum group and its subgroups are obtained with the property of the natural reduction: the differential calculus on the quantum group $GL_q(2,C)$ has to contain…
We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…
We show that the bicrossproduct model $C[SU_2^*]{\blacktriangleright\!\!\triangleleft} U(su_2)$ quantum Poincare group in 2+1 dimensions acting on the quantum spacetime $[x_i,t]=\imath\lambda x_i$ is related by a Drinfeld and module-algebra…
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 mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the shift operators for some one-dimensional exactly solvable potentials in this paper. During such process, a set of method based on original diagonalizing technique…
We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a…
We produce 2-representations of the positive part of affine quantum enveloping algebras on their finite-dimensional counterparts in type $A_n$. These 2-representations naturally extend the right-multiplication 2-representation of…
We study the decomposition matrices for the unipotent $\ell$-blocks of finite special unitary groups SU$_n(q)$ for unitary primes $\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\ldots,10$. We…
The algebra su(2) is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators of the group SU(2). The Wigner-Racah algebra of SU(2) is developed in a…
Quantum state manipulation of two-qubits on the local systems by special unitaries induces special orthogonal rotations on the Bloch spheres. An exact formula is given for determining the local unitaries for some given rotation on the Bloch…
We determine the quantum automorphism groups of finite spaces and find they are all compact quantum groups in the sense of Woronowicz. This solves a problem of Connes for finite spaces.
Let F be a field of characteristic different from $2$, and let $UT_2(F)$ be the algebra of $2\times 2$ upper triangular matrices over $F$. For every involution of the first kind on $UT_2(F)$, we describe the set of all $*$-central…
The quantum group $SU_q(\ell+1)$ has a canonical action on the odd dimensional sphere $S_q^{2\ell+1}$. All odd spectral triples acting on the $L_2$ space of $S_q^{2\ell+1}$ and equivariant under this action have been characterized. This…
Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups -- coordinate functions, differential…
A model of spherically symmetric SU(2) gauge theory is considered. The self-duality equations are written and it is shown that they are compatible with the Einstein-Yang-Mills equations. It is proven that this property is true for any gauge…
Let $D$ be the irreducible bounded symmetric domain of $2\times2$ complex matrices that satisfy $ZZ^* < I_2$. The biholomorphism group of $D$ is realized by $\mathrm{U}(2,2)$ with isotropy at the origin given by…
We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We…
The presentation of two-parameter quantum groups of type E-series in the sense of Benkart-Witherspoon [BW1] is given, which has a Drinfel'd quantum double structure. The universal $R$-matrix and a convex PBW-type basis are described for…