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Smooth Schubert var...
Smooth Schubert varieties and boolean complexes of involutions
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- Umutabazi, Vincent, 1982- (author)
- Linköpings universitet,Algebra, geometri och diskret matematik,Tekniska fakulteten
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- Hultman, Axel, Professor, 1975- (thesis advisor)
- Linköpings universitet,Algebra, geometri och diskret matematik,Tekniska fakulteten
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- Snellman, Jan, Senior Lecturer, 1968- (thesis advisor)
- Linköpings universitet,Algebra, geometri och diskret matematik,Tekniska fakulteten
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- Mazorchuk, Volodymyr, Professor (opponent)
- Department of Mathematics, Algebra and Geometry, Uppsala University, Uppsala, Sweden.
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(creator_code:org_t)
- ISBN 9789179290207
- Linköping : Linköping University Electronic Press, 2021
- English 10 s.
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Series: Linköping Studies in Science and Technology. Licentiate Thesis, 0280-7971 ; 1916
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Abstract
Subject headings
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- This thesis is composed of two papers both in algebraic combinatorics and Coxeter groups.In Paper I, we concentrate on smoothness of Schubert varieties indexed by involutions from finite simply laced types. We show that if a Schubert variety indexed by an involution of a finite and simply laced Coxeter group is smooth, then that involution must be the longest element of a parabolic subgroup.Given a Coxeter system (W, S), we introduce in Paper II the boolean complex of involutions of W as an analogue of the boolean complex of W studied by Ragnarsson and Tenner. By using discrete Morse Theory, we compute the homotopy type for a large class of W, including all finite Coxeter groups. In all cases, the homotopy type is that of a wedge of spheres of dimension |S| − 1. In addition, we provide a recurrence formula for the number of spheres in the wedge.
Subject headings
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Publication and Content Type
- vet (subject category)
- lic (subject category)
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