Symplectic lattice counting and zeta functions of higher Heisenberg groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910247418855424 |
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| author | Shen, Jianhao Voll, Christopher |
| author_facet | Shen, Jianhao Voll, Christopher |
| contents | We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by two distinct invariants, of sublattices of an $\mathfrak{o}$-lattice of finite rank endowed with a non-degenerate symplectic form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23003 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symplectic lattice counting and zeta functions of higher Heisenberg groups Shen, Jianhao Voll, Christopher Group Theory Combinatorics Rings and Algebras 20C08, 11M41, 11S45, 20F18, 17B30, 05A15 We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by two distinct invariants, of sublattices of an $\mathfrak{o}$-lattice of finite rank endowed with a non-degenerate symplectic form. |
| title | Symplectic lattice counting and zeta functions of higher Heisenberg groups |
| topic | Group Theory Combinatorics Rings and Algebras 20C08, 11M41, 11S45, 20F18, 17B30, 05A15 |
| url | https://arxiv.org/abs/2605.23003 |