An analogue of Weyl’s law for quantized irreducible generalized flag manifolds

Abstract

Abstract. We prove an analogue of Weyl's law for quantized irreducible generalized flag manifolds. By this we mean defining a zeta function, similarly to the classical setting, and showing that it satisfies the following two properties: as a functional on the quantized algebra it is proportional to the Haar state; its first singularity coincides with the classical dimension. The relevant formulae are given for the more general case of compact quantum groups.

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On the Dolbeault-Dirac operators on quantum projective spaces

“…On the other hand it is shown in [Mat14] that, by including the modular operator corresponding to the Haar state, one recovers the classical dimension. See also [Mat15] for a discussion of the more general case of quantized irreducible flag manifolds.…”