On the nilpotent representations of \(GL_ n({\mathcal O})\) (Q1325183)
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scientific article; zbMATH DE number 572229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nilpotent representations of \(GL_ n({\mathcal O})\) |
scientific article; zbMATH DE number 572229 |
Statements
On the nilpotent representations of \(GL_ n({\mathcal O})\) (English)
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12 June 1994
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The author constructs some irreducible representations of the profinite group \(GL_ n({\mathcal O})\), where \(\mathcal O\) is the ring of integers in the \(p\)-adic field \(K\). These representations are nilpotent in the sense of his paper [in Commun. Algebra 21, 3529-3543 (1993; Zbl 0788.20026)]. To find them he decomposes a Hecke algebra into ideals by extending combinatorial methods of \textit{P. Delsarte} [J. Comb. Theory, Ser. A 20, 230-343 (1976; Zbl 0342.05020]. The combinatorics enters through the classification by partitions of finite \(\mathcal O\)-modules.
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nilpotent representations
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association scheme
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irreducible representations
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profinite group
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ring of integers
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\(p\)-adic field
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Hecke algebra
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finite \(\mathcal O\)-modules
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