Onn, Uri ; Prasad, Amritanshu ; Vaserstein, Leonid (2006) A Note on Bruhat Decomposition ofGL(n) over Local Principal Ideal Rings Communications in Algebra, 34 (11). pp. 4119-4130. ISSN 0092-7872
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Official URL: http://doi.org/10.1080/00927870600876250
Related URL: http://dx.doi.org/10.1080/00927870600876250
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 A^n. If k is the length of the ring, we determine for which of the pairs (n,k) the double coset space depend 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Taylor and Francis Ltd. |
| ID Code: | 121519 |
| Deposited On: | 19 Jul 2021 06:00 |
| Last Modified: | 19 Jul 2021 06:00 |
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