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Finite-dimensional representations of Uq(osp(1/2n)) and its connection with quantum so(2n+1)

- Rui-bin Zhang
- Mathematics
- 1 August 1992

It is shown that the quantum supergroup Uq(osp(1/2n)) is essentially isomorphic to the quantum group U-q(so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify… Expand

Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n))

- Rui-bin Zhang
- Mathematics
- 1 March 1993

Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n)) at both generic q and q being a root of unity are investigated systematically within the framework of the induced… Expand

THE SECOND FUNDAMENTAL THEOREM OF INVARIANT THEORY FOR THE ORTHOGONAL GROUP

- G. Lehrer, Rui-bin Zhang
- Mathematics
- 16 February 2011

Let V = C n be endowed with an orthogonal form and G = O(V ) be the corresponding orthogonal group. Brauer showed in 1937 that there is a surjective homomorphism : Br(n)! EndG(V r ), where Br(n) is… Expand

Generalized Gel'fand invariants and characteristic identities for quantum groups

- M. Gould, Rui-bin Zhang, A. Bracken
- Mathematics
- 1 September 1991

The generalized Gel’fand invariants for an arbitrary quantum group are explicitly constructed, and their eigenvalues in any irreducible representation are computed. These invariants enable one to… Expand

On Maps Preserving Zero Jordan Products

- M. Chebotar, W. Ke, P. Lee, Rui-bin Zhang
- Mathematics
- 27 February 2006

Abstract.Let R be a ring, A = Mn(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we… Expand

Universal L operator and invariants of the quantum supergroup Uq(gl(m/n))

- Rui-bin Zhang
- Mathematics, Physics
- 1 June 1992

A spectral parameter‐dependent solution of the graded Yang–Baxter equation is obtained, which is universal in the sense that it lives in Uq(gl(m/n))⊗End(V) with V the vector module of Uq(gl(m/n)).… Expand

Analogue of Kostant's u-cohomology formula for the general linear superalgebra

- Shun-Jen Cheng, Rui-bin Zhang
- Mathematics
- 2004

We determine in an explicit form the Lie superalgebra cohomology groups of the upper triangular odd subalgebra (Glm|n)+1 of the general linear superalgebra Glm|n with coefficients in irreducible… Expand

Quantum group invariants and link polynomials

- Rui-bin Zhang, M. Gould, A. Bracken
- Mathematics
- 1991

A general method is developed for constructing quantum group invariants and determining their eigenvalues. Applied to the universalR-matrix this method leads to the construction of a closed formula… Expand

Strongly multiplicity free modules for Lie algebras and quantum groups

- G. Lehrer, Rui-bin Zhang
- Mathematics
- 1 December 2006

Quantum Supergroups and Solutions of the {Yang-Baxter} Equation

- A. Bracken, M. Gould, Rui-bin Zhang
- Physics
- 10 May 1990

A method is developed for systematically constructing trigonometric and rational solutions of the Yang-Baxter equation using the representation theory of quantum supergroups. New quantum R-matrices… Expand

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