Group algebras of reductive $p$-adic groups, their representations and their noncommutative geometry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914103913611264 |
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| author | Solleveld, Maarten |
| author_facet | Solleveld, Maarten |
| contents | This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are:
1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced C*-algebra $C_r^* (G)$.
2. The classification of irreducible G-representations in terms of supercuspidal representations.
3. The Hochschild homology and topological K-theory of these algebras.
In the final part we prove one new result, namely we compute $K_* (C_r^* (G))$ including torsion elements, in terms of equivariant K-theory of compact tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group algebras of reductive $p$-adic groups, their representations and their noncommutative geometry Solleveld, Maarten Representation Theory K-Theory and Homology 20G25, 22E50, 16E40, 19K99, 20C08 This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced C*-algebra $C_r^* (G)$. 2. The classification of irreducible G-representations in terms of supercuspidal representations. 3. The Hochschild homology and topological K-theory of these algebras. In the final part we prove one new result, namely we compute $K_* (C_r^* (G))$ including torsion elements, in terms of equivariant K-theory of compact tori. |
| title | Group algebras of reductive $p$-adic groups, their representations and their noncommutative geometry |
| topic | Representation Theory K-Theory and Homology 20G25, 22E50, 16E40, 19K99, 20C08 |
| url | https://arxiv.org/abs/2510.17260 |