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Monotonicity of strata in the stratification of the cone of totally positive matrices

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  • Amitava Ghosh

    (Durgapur Women’s College)

Abstract

According to a theorem of Bjorner [5], there exists a stratified space whose strata are labeled by the elements of [u, v] for every interval [u, v] in the Bruhat order of a Coxeter group W, and each closed stratum (respectively the boundary of each stratum) has the homology of a ball (respectively of a sphere). In [6], Fomin and Shapiro suggest a natural geometric realization of these stratified spaces for a Weyl group W of a semi-simple Lie group G, and then prove its validity in the case of the symmetric group. The stratified spaces arise as links in the Bruhat decomposition of the totally non-negative part of the unipotent radical of G. In this article, we verify the topological regularity property of the strata formed as a result of Bruhat partial ordering on the elements of theWeyl group (of rank 4) of a semi-simple simply connected algebraic group G which is SL(4,ℝ) in our case here. The Weyl group here is the Coxeter group S 4.

Suggested Citation

  • Amitava Ghosh, 2017. "Monotonicity of strata in the stratification of the cone of totally positive matrices," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(2), pages 245-257, June.
    • Handle: RePEc:spr:indpam:v:48:y:2017:i:2:d:10.1007_s13226-017-0226-7
    DOI: 10.1007/s13226-017-0226-7
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