156 research outputs found
Multiple Flag Varieties of Finite Type
We classify all products of flag varieties with finitely many orbits under
the diagonal action of the general linear group. We also classify the orbits in
each case and construct explicit representatives. This generalizes the
classical Schubert decompostion, which states that the GL(n)-orbits on a
product of two flag varieties correspond to permutations. Our main tool is the
theory of quiver representations.Comment: 18pp. to appear in Adv. Mat
Standard Monomial Theory for Bott-Samelson Varieties of GL(n)
We construct an explicit basis for the coordinate ring of the Bott-Samelson
variety Z_i associated to G = GL(n) and an arbitrary sequence of simple
reflections i. Our basis is parametrized by certain standard tableaux and
generalizes the Standard Monomial basis for Schubert varieties. Our standard
tableaux have a natural crystal graph structure.Comment: Northeastern University, [email protected] AMSTeX amspp
Topological Phenomenology of Space: Architecture as Roots of Infinity
Ideas mature, but interestingly enough, they never get old! It is also notable how are they born. In my case, two elements brought them forward: one question and an admirably unique surrounding
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