0000000001091462

AUTHOR

D. Arnal

showing 2 related works from this author

Star representations of E(2)

1990

We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.

AlgebraUnitary representationRepresentation theory of SURepresentation theory of the Lorentz groupCovering groupZonal spherical functionStatistical and Nonlinear PhysicsUniversal enveloping algebra(gK)-moduleGroup algebraMathematical PhysicsMathematicsLetters in Mathematical Physics
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Geometrical construction of quantum groups representations

2002

We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2, \BbbC)\triangleright \BbbC^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces of polynomial functions with a quadratic relations.

[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA][ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]Mathematics - Quantum AlgebraFOS: Mathematics[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]Quantum Algebra (math.QA)
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