The quantum dilogarithm and unitary representations of cluster modular groupoids
نویسندگان
چکیده
2 The symplectic double of a cluster X -variety 9 2.1 Cluster X and A-varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Construction of the symplectic double . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 A decomposition of mutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 The motivic dilogarithm structure on the symplectic double . . . . . . . . . . . . . . . 16 2.5 The unitary part of the complex double. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
منابع مشابه
The quantum dilogarithm and representations of quantized cluster varieties
To David Kazhdan for his 60th birthday " Loxadь sostoit iz trh neravnyh polovin ". 4 The quantum dilogarithm and its properties 26 4.1 The quantum logarithm function and its properties. . 1 " A horse consists of three unequal halves ". cf. A. de Barr, Horse doctor. Moscow 1868. Cluster varieties [FG2] are relatives of cluster algebras [FZI]. Cluster modular groups act by automor-phisms of clust...
متن کاملSome bounds on unitary duals of classical groups - non-archimeden case
We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups. Roughly, they can show up only if the central character of the inducing irreducible cuspidal representation is dominated by the square root of the modular character of the minimal parabolic subgroup. For unitarizable subquotients...
متن کاملThe quantum dilogarithm and representations of quantum cluster varieties
To David Kazhdan for his 60th birthday " Loxadь sostoit iz trh neravnyh polovin " .
متن کاملCompact quantum groupoids in the setting of C -algebras
We propose a definition of compact quantum groupoids in the setting of C -algebras, associate to such a quantum groupoid a regular C -pseudo-multiplicative unitary, and use this unitary to construct a dual Hopf C -bimodule and to pass to a measurable quantum groupoid in the sense of Enock and Lesieur. Moreover, we discuss examples related to compact and to étale groupoids and study principal co...
متن کاملGeometric quantization of Hamiltonian actions of Lie algebroids and Lie groupoids
We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line bundle. Next, we discuss a version of Kähler quantization suitable for this s...
متن کامل