Abstract
Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of An. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the double coset space depends on the ring in question. For n = 3, we give a complete parametrisation of the double coset space and provide estimates on the rate of growth of the number of double cosets.
Original language | English |
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Pages (from-to) | 4119-4130 |
Number of pages | 12 |
Journal | Communications in Algebra |
Volume | 34 |
Issue number | 11 |
DOIs | |
State | Published - 1 Nov 2006 |
Externally published | Yes |
Keywords
- Bruhat decomposition
- Local rings
- Reduction of matrices
ASJC Scopus subject areas
- Algebra and Number Theory