Combinatorial integers<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E1"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>j</mml:mi></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds

Cenap Özel, Erol Yılmaz

Type: Article

Publication Date: 2006-01-01

Citations: 0

DOI: https://doi.org/10.1155/ijmms/2006/86494

Abstract

We discuss the calculation of integral cohomology ring of L G / T and Ω G . First we describe the root system and Weyl group of L G , then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures of L G / T and Ω G for affine group . We introduce combinatorial integers which play a crucial role in our calculations and give some interesting identities among these integers. Last we calculate generators for ideals and rank of each module of graded integral cohomology algebra in the local coefficient ring ℤ [1/2].

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International Journal of Mathematics and Mathematical Sciences - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View

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Works Cited by This (21)

Action	Title	Year	Authors
+	On the Cohomology Ring of the Infinite Flag Manifold LG/D	1998	Cenap Özel
+	Rational Homotopy Theory of Flag Varieties Associated to Kac-Moody Groups	1985	Shrawan Kumar
+	Constructing Groups Associated to Infinite-Dimensional Lie Algebras	1985	Victor G. Kač
+ PDF Chat	Geometry of Schubert cells and cohomology of Kac-Moody Lie-algebras	1984	Shrawan Kumar
+	Geometry of Coxeter groups	1982	Howard Hiller
+	Introduction to Lie Algebras and Representation Theory	1972	James E. Humphreys
+	Groupes et algèbres de Lie	1971	Nicolás Bourbaki
+ PDF Chat	Infinite-Dimensional Lie Algebras	1990	Victor G. Kač
+ PDF Chat	Infinite flag varieties and conjugacy theorems	1983	Dale H. Peterson Victor G. Kač
+	Reflection Groups and Coxeter Groups	1990	James E. Humphreys