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| Main Author: | |
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| Format: | Preprint |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1410.4992 |
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| _version_ | 1866916518672990208 |
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| author | Ezzat, Shannon |
| author_facet | Ezzat, Shannon |
| contents | This paper is a sequel to "Representation growth of maximal class groups: non-exceptional primes". We use a constructive method to calculate some exceptional cases of $p$-local representation zeta functions of a family of finitely generated nilpotent groups $M_n$ with maximal nilpotency class. Using the machinery of the constructive method from the prequel paper we construct all irreducible representations of degree $p^N$ for all $N\in \mathbb{N}$ for the group $M_{p+1}$ for a fixed prime $p$. We also construct all irreducible representations of degree $2^N$ for the group $M_4$. Together with the main result from the prequel, this gives us a complete understanding of the irreducible representations of the groups $M_3$ and $M_4$, along with their global representation zeta functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1410_4992 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Representation growth of maximal class groups: various exceptional cases Ezzat, Shannon Group Theory This paper is a sequel to "Representation growth of maximal class groups: non-exceptional primes". We use a constructive method to calculate some exceptional cases of $p$-local representation zeta functions of a family of finitely generated nilpotent groups $M_n$ with maximal nilpotency class. Using the machinery of the constructive method from the prequel paper we construct all irreducible representations of degree $p^N$ for all $N\in \mathbb{N}$ for the group $M_{p+1}$ for a fixed prime $p$. We also construct all irreducible representations of degree $2^N$ for the group $M_4$. Together with the main result from the prequel, this gives us a complete understanding of the irreducible representations of the groups $M_3$ and $M_4$, along with their global representation zeta functions. |
| title | Representation growth of maximal class groups: various exceptional cases |
| topic | Group Theory |
| url | https://arxiv.org/abs/1410.4992 |