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

Uri Onn; Amritanshu Prasad; Leonid Vaserstein

doi:10.1080/00927870600876250

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

Uri Onn, Amritanshu Prasad, Leonid Vaserstein

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Let A be a local commutative principal ideal ring. We study the double coset space of GL_n(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
Pages (from-to)	4119-4130
Number of pages	12
Journal	Communications in Algebra
Volume	34
Issue number	11
DOIs	https://doi.org/10.1080/00927870600876250
State	Published - 1 Nov 2006
Externally published	Yes

Keywords

Bruhat decomposition
Local rings
Reduction of matrices

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870600876250

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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.",

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AU - Onn, Uri

AU - Prasad, Amritanshu

AU - Vaserstein, Leonid

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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.

KW - Bruhat decomposition

KW - Local rings

KW - Reduction of matrices

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EP - 4130

JO - Communications in Algebra

JF - Communications in Algebra

IS - 11

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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