A filtration of the loops on SU\((N)\) by Schubert varieties

DOI10.1007/BF01229802zbMath0613.57025MaRDI QIDQ1819422

Stephen A. Mitchell

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173790

zbMATH Keywords

Schubert varietiesloop groupsThom spacesintegral homology of \(\Omega \) SU\((n)\)

Mathematics Subject Classification ID

(H)-spaces and duals (55P45) Homology and cohomology of (H)-spaces (57T25)

Related Items

A filtration of algebraic loops ⋮ Multiplicative structure in the stable splitting of \(\Omega S L_n(\mathbb{C})\) ⋮ Splitting ℂP^∞ and Bℤ/pⁿ into Thom spectra ⋮ Connectivity properties of moment maps on based loop groups ⋮ Connectedness of levels for moment maps on various classes of loop groups ⋮ Pattern characterization of rationally smooth affine Schubert varieties of type \(A\) ⋮ The module structure of the equivariant \(K\)-theory of the based loop group of \(SU(2)\) ⋮ Bott periodicity and stable quantum classes ⋮ Thin loop groups ⋮ Rationally smooth elements of Coxeter groups and triangle group avoidance. ⋮ The Bruhat order, the lookup conjecture and spiral Schubert varieties of type \(\tilde{A}_2\) ⋮ \(\Omega\)SU(3) splits after four suspensions, but not two ⋮ The loops onU(n)/O(n) andU(2n)/Sp(n) ⋮ Combinatorial integers \(\binom{m,n}{j}\) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds ⋮ Smooth Schubert varieties in the affine flag variety of type \(\tilde{A}\) ⋮ Smooth and palindromic Schubert varieties in affine Grassmannians ⋮ Generating varieties for affine Grassmannians ⋮ Common subbundles and intersections of divisors

Cites Work

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• The space of loops on a Lie group
• Decompositions of the space of loops on a Lie group
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• An application of the Morse theory to the topology of Lie-groups
• Désingularisation des variétés de Schubert généralisées
• A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott
• Infinite flag varieties and conjugacy theorems