TY - JOUR
T1 - A note on Bruhat decomposition of GL(n) over local principal ideal rings
AU - Onn, Uri
AU - Prasad, Amritanshu
AU - Vaserstein, Leonid
PY - 2006/11/1
Y1 - 2006/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33845205344&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33845205344&partnerID=8YFLogxK
U2 - 10.1080/00927870600876250
DO - 10.1080/00927870600876250
M3 - Article
AN - SCOPUS:33845205344
SN - 0092-7872
VL - 34
SP - 4119
EP - 4130
JO - Communications in Algebra
JF - Communications in Algebra
IS - 11
ER -