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

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.

21 pages, comments are welcome

References in corpus (3)

• Quantum Dimension and Quantum Projective Spaces
• On the Dolbeault--Dirac Operator of Quantized Symmetric Spaces
• Non-commutative integration, zeta functions and the Haar state for $S{U}_q(2)$

Cited by in corpus (1)

• LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory