Minimal and maximal elements in Kazhdan-Lusztig double sided cells of Sn and Robinson-Schensted correspondence
نویسنده
چکیده
In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of these sets with tableau, using the RobinsonSchensted correspondence. We show also that the set of elements of maximal length in a two sided cell is the set of longest minimal right coset representatives of conjuagted parabolic subgroups.
منابع مشابه
Minimal and maximal elements in Kazhdan-Lusztig double sided cells of Sn and a Robinson-Schensted correspondance in simply laced Coxeter groups
Let W be a Coxeter group. We generalise the Knuth plactic relations to W and we show that their equivalence classes decompose the Kazhdan-Lusztig cells. In the case of symmetric groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with ...
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In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with tableau, using the RobinsonSchensted correspondance. We show also that the set of elements of maximal length in a two sided cell is the set...
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