Mathematics

Reports outline mathematics study findings from University of Iowa

  2008 NOV 24 - (VerticalNews.com) -- According to a study from the United States, "This paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t(1), t(2)..., t(n)]."

  "We show these group actions are the same as an action of simple transpositions studied geometrically by M. Brion, and give topological meaning to the divided difference operators of Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and others. We analyze these representations using the combinatorial approach to equivariant cohomology introduced by Goresky-Kottwitz-MacPherson," wrote J.S. Tymoczko and colleagues, University of Iowa.

  The researchers concluded: "We find that each permutation representation on equivariant cohomology produces a representation on ordinary cohomology that is trivial, though the equivariant representation is not."

  Tymoczko and colleagues published the results of their research in American Journal of Mathematics (Permutation representations on Schubert varieties. American Journal of Mathematics, 2008;130(5):1171-1194).

  For additional information, contact J.S. Tymoczko, University of Iowa, Dept. of Math, Iowa City, IA 52242, USA.

  The publisher of the American Journal of Mathematics can be contacted at: Johns Hopkins University Press, Journals Publishing Division, 2715 North Charles St., Baltimore, MD 21218-4363, USA.

  Keywords: Combinatorial, Combinatoric, Emerging Technologies, Machine LearningMathematics, University of Iowa.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.