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arXiv · 1606.01827

Dolbeault-Dirac operators, quantum Clifford algebras and the Parthasarathy formula

Marco Matassa
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Abstract

We consider Dolbeault-Dirac operators on quantized irreducible flag manifolds as defined by Kr\"ahmer and Tucker-Simmons. We show that, in general, these operators do not satisfy a formula of Parthasarathy-type. This is a consequence of two results that we prove here: we always have quadratic commutation relations for the relevant quantum root vectors, up to terms in the quantized Levi factor; there are examples of quantum Clifford algebras where the commutation relations are not of quadratic-constant type.

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Marco Matassa. 2016-06-06. Dolbeault-Dirac operators, quantum Clifford algebras and the Parthasarathy formula. https://doi.org/10.1007/s00006-016-0730-6

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