Seminar on Algebraic Geometry: On Bruhat decomposition over local principal ideal rings
Dr. Amritanshu Prasad
Institute of Mathematical Sciences, Chennai.
The permutation matrix associated to an invertible matrix is a complete invariant of its double coset with respect to upper triangular matrices in the general linear group. This fails for rings in general. We discuss some partial invariants and describe some new "Schubert varieties" associated to these invariants.