Summary
In Chap. 9 we give the analogous theory over the p-adic, giving the decomposition of the representation of GL d (ℤ p ) afforded by the p-adic Grassmannian. The relative position of two planes p, q ⊆ ℤ p d is given by the type of the ℤ p -module p ∩ q, i.e., by a partition. We calculate the measure on Ω m d, and describe the idempotents — the p-adic multivariable Jacobi polynomials.
Keywords
- Unitary Representation
- Direct Limit
- Harmonic Measure
- Inverse Limit
- Maximal Compact Subgroup
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). p-Adic Grassmann Manifold. In: Haran, S.M.J. (eds) Arithmetical Investigations. Lecture Notes in Mathematics, vol 1941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78379-4_10
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DOI: https://doi.org/10.1007/978-3-540-78379-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78378-7
Online ISBN: 978-3-540-78379-4
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