Coherent States for Quantum Compact Groups

Details Coherent States for Quantum Compact Groups Coherent States for Quantum Compact Groups

1994-03-19

arxiv.org/abs/hep-th/9403114v1

Commun.Math.Phys.182:221-251,1996

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1007/BF02506391

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the $q$--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}

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