A Note on Bruhat Decomposition ofGL(n) over Local Principal Ideal Rings

DOI10.1080/00927870600876250zbMath1112.15020arXivmath/0506094OpenAlexW3101186226MaRDI QIDQ3422840

Uri Onn, Amritanshu Prasad, L.N.Vaserstein and E.R.Wheland

Publication date: 14 February 2007

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506094

zbMATH Keywords

parametrizationlocal ringscommutative ringstabilizerintersection invariantsflagsBruhat decompositionreduction of matricesdouble coset space

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Regular local rings (13H05) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (7)

On branching rules of depth-zero representations ⋮ Geometric interpretation of Murphy bases and an application. ⋮ Principal series for general linear groups over finite commutative rings ⋮ Continuous maps on triangular matrices that preserve commutativity ⋮ A multiplicity one theorem for groups of type 𝐴_{𝑛} over discrete valuation rings ⋮ Gelfand criterion and multiplicity one results for \(\mathrm{GL}_n\) over finite chain rings ⋮ Branching rules for unramified principal series representations of GL(3) over a \(p\)-adic field

Cites Work

• Submodule categories of wild representation type.
• Representations of finite classical groups. A Hopf algebra approach
• Chain categories of modules and subprojective representations of posets over uniserial algebras.
• Regular elements and regular characters of \(GL_ n({\mathcal O})\)
• Bounded submodules of modules.
• A jordan decomposition of representations forGL_n(O)

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