On the centre of two-parameter quantum groups <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="fraktur">g</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> for type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="sc

Irreducible tensor operators as the irreducible submodules of an adjoint representation of the two-parametric quantum ∗-algebra [Formula: see text] are constructed by using its Jordan–Schwinger formulation on two independent [Formula: see text]-oscillator ∗-algebras. All [Formula: see text]-submodules are equipped with an appropriate Hilbert–Schmidt scalar product with the help of the Wigner–Eckart theorem. We show that with respect to this scalar product, not only the bases of all irreducible submodules of the adjoint representation are orthonormal, but also the adjoint representation is a ∗-representation.

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On the centre of two-parameter quantum groups Ur,s(g) for type
Naihong Hu
¹
,
Yuxing Shi
²

Cited by 3 publications

References 22 publications

Two-parameter quantum affine algebra of type Cn(1), Drinfeld realization and vertex representation

Two-parameter quantum affine algebra of type Cn(1), Drinfeld realization and vertex representation

Quantum supergroup Ur,s(osp(1,2)), Scasimir operators and Dickson polynomials

From the Wigner–Eckart theorem to the Hilbert–Schmidt scalar product for an adjoint representation of the quantum algebra Up,q(su2)

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On the centre of two-parameter quantum groups Ur,s(g) for type Naihong Hu1, Yuxing Shi2

Cited by 3 publications

References 22 publications

Two-parameter quantum affine algebra of type Cn(1), Drinfeld realization and vertex representation

Two-parameter quantum affine algebra of type Cn(1), Drinfeld realization and vertex representation

Quantum supergroup Ur,s(osp(1,2)), Scasimir operators and Dickson polynomials

From the Wigner–Eckart theorem to the Hilbert–Schmidt scalar product for an adjoint representation of the quantum algebra Up,q(su2)

Contact Info

Product

Resources

About

On the centre of two-parameter quantum groups Ur,s(g) for type
Naihong Hu
¹
,
Yuxing Shi
²