We study the formal geometric quantization of $$b^m$$ -symplectic manifolds equipped with Hamiltonian actions of a torus T with nonzero leading modular weight. The resulting virtual $$T-$$ modules are finite dimensional when m is odd, as in [4]; when m is even, these virtual modules are not finite dimensional, and we compute the asymptotics of the representations for large weight.

中文翻译：

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$$b^m$$-辛流形的几何量化

我们研究了 $$b^m$$ -辛流形的形式几何量化，该流形配备了具有非零领先模权重的环面 T 的哈密顿行为。当 m 为奇数时，生成的虚拟 $$T-$$ 模块是有限维的，如 [4] 中所示；当 m 是偶数时，这些虚拟模块不是有限维的，我们计算大权重的表示的渐近性。