Tiêu đề | Generic semistability for reductive group actions |
Loại công bố | Journal Article |
Năm xuất bản | 2016 |
Tác giả | Bac, DPhuong, Hyeon, D |
Tạp chí | Proc. Am. Math. Soc. |
Thể tích | 144 |
Trang | 4115–4124 |
Tóm tắt | We prove that given a reductive algebraic group G G and a rational representation ρ : G $\rightarrow$ G L ( V ) \textbackslashrho : G \textbackslashto \textbackslashmathrm {GL}(V) defined over an algebraically closed field of characteristic 0 0 , v $\in$ V v \textbackslashin V is generically semistable, i.e., 0 $\not\in$ T . v \textasciimacron 0 \textbackslashnot \textbackslashin \textbackslashoverline {T.v} for a general maximal torus T T if and only if v v is semistable with respect to the induced action of the center of G G . The proof is obtained through a detailed description of the relation between the state polytope with respect to the maximal torus T T of G G and the state polytope with respect to T $\cap$ [ G , G ] T \textbackslashcap [G,G] . We also consider the case of solvable groups and prove that the generic semistability implies the center semistability but not the other way around. |