arXiv subjects

T. D. Palev

Publications and source records attributed to T. D. Palev.

39 records · Page 3Linked to original sources

arXiv1993

Finite Dimensional Representations of the Quantum Superalgebra $U_q[gl(3/2)]$ in a Reduced $U_q[gl(3/2)] \supset U_q[gl(3/1)] \supset U_q[gl(3)]$ Basis

For generic $q$ we give expressions for the transformations of all essentially typical finite-dimensional modules of the Hopf superalgebra $U_q[gl(3/2)]$. The latter is a deformation of the universal enveloping algebra of the Lie superalgebra $gl(3/2)$. The basis within each module is similar to the Gel'fand-Zetlin basis for $gl(5)$. We write down expressions for the transformations of the basis under the action of the Chevalley generators.

hep-th↗

arXiv1993

A Superalgebra Morphism of Uq[OSP(1/2N)] onto the Deformed Oscillator Superalgebra Wq(N)

We prove that the deformed oscillator superalgebra $W_q(n)$ (which in the Fock representation is generated essentially by $n$ pairs of $q$-bosons) is a factor algebra of the quantized universal enveloping algebra $U_q[osp(1/2n)]$. We write down a $q$-analog of the Cartan-Weyl basis for the deformed $osp(1/2n)$ and give also an oscillator realization of all Cartan-Weyl generators.

hep-th↗

arXiv1993

On a possible algebra morphism of U$_q$[OSP(1/2N)] onto the deformed oscillator algebra W$_q$(N)

We formulate a conjecture, stating that the algebra of $n$ pairs of deformed Bose creation and annihilation operators is a factor-algebra of $U_q[osp(1/2n)]$, considered as a Hopf algebra, and prove it for $n=2$ case. To this end we show that for any value of $q$ $U_q[osp(1/4)]$ can be viewed as a superalgebra, freely generated by two pairs $B_1^\pm$, $B_2^\pm$ of deformed para-Bose operators. We write down all Hopf algebra relations, an analogue of the Cartan-Weyl basis, the "commutation" relations between the generators and a basis in $U_q[osp(1/2n)]$ entirely in terms of $B_1^\pm$, $B_2^\pm$.

hep-th↗