Intersection and Incidence Distances Between Parabolic Subgroups of a Reductive Group
- 作者: Gordeev N.1, Rehmann U.2
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隶属关系:
- Russian State Pedagogical University, St.Petersburg State University
- Department of Mathematics, Bielefeled University
- 期: 卷 219, 编号 3 (2016)
- 页面: 405-412
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238587
- DOI: https://doi.org/10.1007/s10958-016-3116-3
- ID: 238587
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详细
Let Γ be a reductive algebraic group, and let P,Q ⊂ Γ be a pair of parabolic subgroups. Some properties of the intersection and incidence distances \( \begin{array}{c}\hfill {\mathrm{d}}_{\mathrm{in}}\left(P,Q\right)= \max \left\{ \dim P, \dim Q\right\}- \dim \left(P\cap Q\right),\hfill \\ {}\hfill {\mathrm{d}}_{\mathrm{in}\mathrm{c}}\left(P,Q\right)=\mathrm{mix}\left\{ \dim P, \dim Q\right\}- \dim \left(P\cap Q\right)\hfill \end{array} \) are considered (if P,Q are Borel subgroups, both numbers coincide with the Tits distance dist(P,Q) in the building Δ(Γ) of all parabolic subgroups of Γ). In particular, if Γ = GL(V ) and P = Pv,Q = Pu are stabilizers in GL(V ) of linear subspaces v, u ⊂ V , we obtain the formula din(P, Q) = − d2 + a1d + a2, where d = din(v, u) = max{dim v, dim u} − dim(v ∩ u) is the intersection distance between the subspaces v and u and where a1 and a2 are integers expressed in terms of dim V , dim v, and dim u. Bibliography: 7 titles.
作者简介
N. Gordeev
Russian State Pedagogical University, St.Petersburg State University
编辑信件的主要联系方式.
Email: nickgordeev@mail.ru
俄罗斯联邦, St.Petersburg
U. Rehmann
Department of Mathematics, Bielefeled University
Email: nickgordeev@mail.ru
德国, Bielefeld