Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras

Let g be a semi-simple Lie algebra with fixed root system, and Uq(g) the quantization of its universal enveloping algebra. Let S be a subset of the simple roots of g. We show that the defining relations for Uq(g) can be slightly modified in such a way that the resulting algebra Uq(g;S) allows a homomorphism onto (an extension of) the algebra Pol(Gq/KS,q) of functions on the quantum flag manifold Gq/KSq corresponding to S. Moreover, this homomorphism is equivariant with respect to a natural adjoint action of Uq(g) on Uq(g;S) and the standard action of Uq(g) on Pol(Gq/KSq).

Jaar van publicatie:2015

Trefwoorden:Quantum groups

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