The Peterson variety and the wonderful compactification
نویسندگان
چکیده
منابع مشابه
Partitions of the Wonderful Group Compactification
We define and study a family of partitions of the wonderful compactification G of a semi-simple algebraic group G of adjoint type. The partitions are obtained from subgroups of G × G associated to triples (A1, A2, a), where A1 and A2 are subgraphs of the Dynkin graph Γ of G and a : A1 → A2 is an isomorphism. The partitions of G of Springer and Lusztig correspond respectively to the triples (∅, ...
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We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne-Lusztig (or AlvisCurtis) duality for p-adic groups to homological duality. This provides a new way to introduce an involution on the set of irreducible representations of the group, which has been earlier defined by A. Zelevinsky for G = GL(n) by A.-M. Aubert in general. As a byproduct we des...
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Fix a nonsingular algebraic variety Y over an algebraically closed field (of arbitrary characteristic). An arrangement of subvarieties S is a finite collection of nonsingular subvarieties such that all nonempty scheme-theoretic intersections of subvarieties in S are again in S, or equivalently, such that any two subvarieties intersect cleanly and the intersection is either empty or a subvariety...
متن کاملThe G-stable Pieces of the Wonderful Compactification
Let G be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification Ḡ of G into finite many G-stable pieces, which was introduced by Lusztig. In this paper, we will investigate the closure of any G-stable piece in Ḡ. We will show that the closure is a disjoint union of some G-stable pieces, which was first conjectured by Luszti...
متن کاملSchubert Calculus and the Homology of the Peterson Variety
We use the tight correlation between the geometry of the Peterson variety and the combinatorics the symmetric group to prove that homology of the Peterson variety injects into the homology of the flag variety. Our proof counts the points of intersection between certain Schubert varieties in the full flag variety and the Peterson variety, and shows that these intersections are proper and transve...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2017
ISSN: 1088-4165
DOI: 10.1090/ert/499