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.

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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 -