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Proceedings of the London Mathematical Society (1)

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The locally finite part of the dual coalgebra of quantized irreducible flag manifolds
I. Heckenberger, S. Kolb
Journal:

Proceedings of the London Mathematical Society / Volume 89 / Issue 2 / September 2004

Published online by Cambridge University Press:

08 September 2004, pp. 457-484

Print publication:

September 2004
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For quantized irreducible flag manifolds the locally finite part of the dual coalgebra is shown to coincide with a natural quotient coalgebra $\overline{U}$ of $U_q ( \mathfrak{g} )$. On the way the coradical filtration of $\overline{U}$ is determined. A graded version of the duality between $\overline{U}$ and the quantized coordinate ring is established. This leads to a natural construction of several examples of quantized vector spaces.
As an application, covariant first order differential calculi on quantized irreducible flag manifolds are classified.