Parabolic extensions of the Hecke ring for the general linear group. II. (Russian. English summary) Zbl 0748.11026
[For Part I, cf. ibid. 154, 36-45 (1986; Zbl 0613.10029.)]
The Hecke ring for the group \(GL_ n({\mathcal O})\), \(n\geq 1\), \({\mathcal O}\) is the ring of integers in the finite extension of a field \(\mathbb{Q}_ p\), is considered. Sufficient conditions for the reducibility of polynomials over a parabolic extension of this ring are given. As an example an explicit formula is proved for the factorization of the polynomial of degree 6 over the Hecke \(p\)-ring of the unitary group \(SU(2,2)\) for a prime \(p\) which is decomposable in an imaginary quadratic field.
The Hecke ring for the group \(GL_ n({\mathcal O})\), \(n\geq 1\), \({\mathcal O}\) is the ring of integers in the finite extension of a field \(\mathbb{Q}_ p\), is considered. Sufficient conditions for the reducibility of polynomials over a parabolic extension of this ring are given. As an example an explicit formula is proved for the factorization of the polynomial of degree 6 over the Hecke \(p\)-ring of the unitary group \(SU(2,2)\) for a prime \(p\) which is decomposable in an imaginary quadratic field.
Reviewer: N.V.Kuznetsov (Khabarovsk)
MSC:
| 11F60 | Hecke-Petersson operators, differential operators (several variables) |
| 20G25 | Linear algebraic groups over local fields and their integers |
