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- W4281639017 abstract "Let us consider, for $$n ge 3$$ , the Cartan domain $$mathrm {D}_n^{mathrm {IV}}$$ of type IV. On the weighted Bergman spaces $$mathcal {A}^2_lambda (mathrm {D}_n^{mathrm {IV}})$$ we study the problem of the existence of commutative $$C^*$$ -algebras generated by Toeplitz operators with special symbols. We focus on the subgroup $$mathrm {SO}(n) times mathrm {SO}(2)$$ of biholomorphisms of $$mathrm {D}_n^{mathrm {IV}}$$ that fix the origin. The $$mathrm {SO}(n) times mathrm {SO}(2)$$ -invariant symbols yield Toeplitz operators that generate commutative $$C^*$$ -algebras, but commutativity is lost when we consider symbols invariant under a maximal torus or under $$mathrm {SO}(2)$$ . We compute the moment map $$mu ^{mathrm {SO}(2)}$$ for the $$mathrm {SO}(2)$$ -action on $$mathrm {D}_n^{mathrm {IV}}$$ considered as a symplectic manifold for the Bergman metric. We prove that the space of symbols of the form $$a = f circ mu ^{mathrm {SO}(2)}$$ , denoted by $$L^infty (mathrm {D}_n^{mathrm {IV}})^{mu ^{mathrm {SO}(2)}}$$ , yield Toeplitz operators that generate commutative $$C^*$$ -algebras. Spectral integral formulas for these Toeplitz operators are also obtained." @default.
- W4281639017 created "2022-06-13" @default.
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- W4281639017 date "2022-09-27" @default.
- W4281639017 modified "2023-10-09" @default.
- W4281639017 title "Commuting Toeplitz Operators on Cartan Domains of Type IV and Moment Maps" @default.
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- W4281639017 doi "https://doi.org/10.1007/s11785-022-01280-1" @default.
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