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The locally finite part of the dual coalgebra of quantized irreducible flag manifolds

Published online by Cambridge University Press:  08 September 2004

I. Heckenberger  and
S. Kolb
I. Heckenberger
Affiliation:
Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany. E-mail: Istvan.Heckenberger@math.uni-leipzig.de
S. Kolb
Affiliation:
Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany. E-mail: kolb@itp.uni-leipzig.de
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Abstract

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.

Keywords

quantum groupsquantized flag manifolds58B32 (primary)81R50 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 89 , Issue 2 , September 2004 , pp. 457 - 484
Copyright
2004 London Mathematical Society

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