The wonderful compactification for quantum groups
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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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...
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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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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...
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In a previous paper [K1] I have constructed a compactification KGLn of the general linear group GLn, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De Concini and Procesi. In particular there is an action of G = GLn × GLn on this compactification. In this paper we show how the space of global section of an arb...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2018
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12193