Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups
| Autor: | Sardar Pranab, S. S. Kannan |
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| Rok vydání: | 2009 |
| Předmět: |
Ample line bundle
Mathematics::Number Theory General Mathematics Picard group GIT quotient Torus General linear group Combinatorics Algebra Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Symmetric group Mathematics::Quantum Algebra FOS: Mathematics 14Lxx Maximal torus Representation Theory (math.RT) Mathematics::Representation Theory Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics - Representation Theory Quotient Mathematics |
| Zdroj: | Proceedings - Mathematical Sciences. 119:81-100 |
| ISSN: | 0973-7685 0253-4142 |
| DOI: | 10.1007/s12044-009-0009-0 |
| Popis: | We give a stratification of the GIT quotient of the Grassmannian $G_{2,n}$ modulo the normaliser of a maximal torus of $SL_{n}(k)$ with respect to the ample generator of the Picard group of $G_{2,n}$. We also prove that the flag variety $GL_{n}(k)/B_{n}$ can be obtained as a GIT quotient of $GL_{n+1}(k)/B_{n+1}$ modulo a maximal torus of $SL_{n+1}(k)$ for a suitable choice of an ample line bundle on $GL_{n+1}(k)/B_{n+1}$. 19 pages |
| Databáze: | OpenAIRE |
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