Cell Decompositions of the Special Orthogonal Algebraic Monoids
Zhenheng Li · Communications in Algebra · 2003
Let MSO n (n is even) be the special orthogonal algebraic monoid, B a Borel subgroup of its unit group. We take a more direct definition of cells for MSO n in terms of B × B-orbits and explicitly determine the cell decompositions of MSO n . It turns out that each cell is the intersection of MSO n with a cell of M n (K), the monoid of all n×n matrices over an algebraically closed field K.