Heat Kernel on Lie Groups and Maximally Symmetric Spaces

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Focusing on the heat kernel for spin-tensor Laplacians, this monograph presents innovative methods and tools while compiling known exact results for spheres and hyperbolic spaces. It is divided into two parts: the first delves into the geometry of simple Lie groups and maximally symmetric spaces, while the second covers the computation of heat kernels for various Laplacians across different dimensions. This work serves as a crucial resource for researchers and graduate students in mathematics and theoretical physics, encompassing diverse fields such as spectral geometry and quantum gravity.