arXiv math/99090671999-09-14math.QAhep-thmath-phmath.MPmath.RT

Two-parametric deformation $U_{p,q}[gl(2/1)]$ and its induced representations

Nguyen Anh Ky

备注：: Latex, 13 pages, no figure
发表信息：: J.Phys.A29:1541,1996
DOI：: 10.1088/0305-4470/29/7/022

英文摘要：

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical) finite-dimensional representations of this quantum superalgebra. In spite of some specific features, the present approach is similar to a previously developed method [1] which, as shown here, is applicable not only to the one-parametric quantum deformations but also to the multi-parametric ones.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A three-parametric deformation of GL(1/1)

A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra $U[gl(1/1)]$.

2005-10-11hep-thmath-phmath.MP

Some deformations of U[sl(2)] and their representations

Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters.

2003-11-15hep-thmath-phmath.MP

A two-parametric deformation of U[sl(2)], its representations and complex "spin"

A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters. Interestingly that finite-dimensional representations of $U_{pq}[sl(2)]$ allow arbitrary complex "spins" (i.e., not necessary they to be integral or half-integral numbers), unlike those in the classical and one-parametric deformation cases.

2005-07-15hep-thmath-phmath.MP

Manin matrices of type C: multi-parametric deformation

We constructed a multi-parametric deformation of the Brauer algebra representation related with the symplectic Lie algebras. The notion of Manin matrix of type C was generalised to the case of the multi-parametric deformation by using this representation and corresponding quadratic algebras. We derived pairing operators for these quadratic algebras and minors for the considered Manin matrices. The rank of pairing operators and dimensions of components of quadratic algebras were calculated.

2022-03-24math-phmath.MPmath.QA

Induced Representations of the Two Parametric Quantum Deformation U$_{pq}$[gl(2/2)]

The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in detail. It turns out that finite-dimensional representations of the two-parametric $U_{p,q}[gl(2/2)]$, even at generic deformation parameters, are not simply trivial deformations from those of the classical superalgebra $gl(2/2)$, unlike the one-parametric cases.

2000-05-12hep-thmath-phmath.GR

Two-parametric extension of h-deformation of GL$(1| 1)$

The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.

2001-12-06math.DGmath.QA

更多相关论文收起更多论文

Drinfeld twist for two-parametric deformation of gl(2) and sl(1/2)

Drinfeld twist is applied to the Lie algebra gl(2) so that a two-parametric deformation of it is obtained, which is identical to the Jordanian deformation of the gl(2) obtained by Aneva et al. The same twist element is applied to deform the Lie superalgebra sl(1/2), since the gl(2) is embedded into the sl(1/2). By making use of the FRT-formalism, we construct a deformation of the Lie supergroup $ SL(1/2). $

1998-07-10math.QA

Superalgebras, their quantum deformations and the induced representation method

Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have succeeded in constructing representations of several higher rank superalgebras. When representations of quantum superalgebras are concerned, we have developed a method which can be applied not only to the one-parametric quantum deformations but also to the multi-parametric ones. As an intermediate step the Gel'fand-Zetlin basis description is extended to the…

1998-10-29hep-thmath-phmath.MP

Irreducible representations of Upq[gl(2/2)]

The two-parametric quantum superalgebra $U_{pq}[gl(2/2)]$ and its representations are considered. All finite-dimensional irreducible representations of this quantum superalgebra can be constructed and classified into typical and nontypical ones according to a proposition proved in the present paper. This proposition is a nontrivial deformation from the one for the classical superalgebra gl(2/2), unlike the case of one-parametric deformations.

2001-04-12hep-thmath-phmath.MP

On The Inhomogeneous Quantum Groups

Using the multi-parametric deformation of the algebra of functions on $ \GL{n+1} $ and the universal enveloping algebra $ \U{\igl{n+1}} $, we construct the multi-parametric quantum groups $ \IGLq{n} $ and $ \Uq{\igl{n}} $.

1994-09-22hep-thmath.QA

On Hopf-induced deformation of topological locus

We provide a very brief review of the description of colored invariants for the Hopf link in terms of characters, which need to be taken at a peculiar deformation of the topological locus, depending on one of the two representations associated with the two components of the link. Most important, we extend the description of this locus to conjugate and, generically, to composite representations and also define the "adjoint" Schur functions emerging in the dual description.

2018-04-26hep-thmath.GTmath.QA

Quantum Deformation of igl(n) Algebra on Quantum Space

We study quantum deformed $gl(n)$ and $igl(n)$ algebras on a quantum space discussing multi-parametric extension. We realize elements of deformed $gl(n)$ and $igl(n)$ algebras by a quantum fermionic space. We investigate a map between deformed $igl(2)$ algebras of our basis and other basis.

1996-10-21hep-thmath.QAq-alg

Deformation of Yangian $Y(sl_2)$

A quantization of a non-standard rational solution of CYBE for $sl_2$ is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian $Y(sl_2$. This quantum object (deformed Yangian $Y_{η,ξ}(sl_2))$ is a two-parametric deformation of the universal enveloping algebra $U(sl_2[u])$ of the positive current algebra $sl_2[u]$. We consider the pseudotriangular structure on $Y_{η,ξ}(sl_2)$, the quantum double $DY_{η,ξ}(sl_2)$ its the universal R-matrix and also the RTT-realization of $Y_{η,ξ}(sl_2)$.

1995-11-10math.QAq-alg