Partitions of the wonderful group compactification

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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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On Intersections of Certain Partitions of a Group Compactification

Let G be a connected semi-simple algebraic group of adjoint type over an algebraically closed field, and let G be the wonderful compactification of G. For a fixed pair (B, B−) of opposite Borel subgroups of G, we look at intersections of Lusztig’s G-stable pieces and the B−×B-orbits in G, as well as intersections of B ×B-orbits and B− ×B−-orbits in G. We give explicit conditions for such inters...

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ژورنال

عنوان ژورنال: Transformation Groups

سال: 2007

ISSN: 1083-4362,1531-586X

DOI: 10.1007/s00031-007-0062-7