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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Canadian Journal of Mathematics
( Vol. 51 NO.3 / (1999))
Parabolic Subgroups with Abelian Unipotent Radical as a Testing Site for Invariant Theory
Dmitri I. Panyshev,
Pages. 616-635
Abstract Let $L$ be a simple algebraic group and $P$ a parabolic subgroup with Abelian unipotent radical $P^u$. Many familiar varieties (determinantal varieties, their
symmetric and skew-symmetric analogues) arise as closures of $P$-orbits in
$P^u$. We give a unified invariant-theoretic treatment of various properties of
these orbit closures. We also describe the closures of the conormal bundles of
these orbits as the irreducible components of some commuting variety and show
that the polynomial algebra $k[P^u]$ is a free module over the algebra of
covariants.
Contents Introduction
Notation and conventions
1. Canonical strings of roots and their properties
2. Resolution of singularities of the closures of $G$-orbits in $mathfrak l$(1)
3. The commuting variety and a double coset space
4. The algebra of covariants on $mathfrak l$(1) and beyond
5. On equidimensional quotient mappings
Appendix
Key words
Mathmatical Subject Classification 14L30, 13A50