A note on Bruhat decomposition of GL(n) over local principal ideal rings

Uri Onn, Amritanshu Prasad, Leonid Vaserstein

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7 Scopus citations

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 languageEnglish (US)
Pages (from-to)4119-4130
Number of pages12
JournalCommunications in Algebra
Volume34
Issue number11
DOIs
StatePublished - Nov 1 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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