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arXiv · 2309.09935

Homology of loops on a splitting-rank symmetric space via the Geometric Satake for real groups

John O'Brien
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Abstract

Using Nadler's Geometric Satake Equivalence for real reductive groups, we obtain a description of the equivariant homology of the loop space of splitting-rank symmetric spaces in terms of the relative dual group of the space. The description is in line with Yun and Zhu's calculation for the loop space of a compact Lie group. The formula hints at a relative duality for these spaces.

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John O'Brien. 2023-09-18. Homology of loops on a splitting-rank symmetric space via the Geometric Satake for real groups. https://arxiv.org/abs/2309.09935

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