کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4605982 1337673 2014 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hitchin's conjecture for simply-laced Lie algebras implies that for any simple Lie algebra
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Hitchin's conjecture for simply-laced Lie algebras implies that for any simple Lie algebra
چکیده انگلیسی

Let gg be any simple Lie algebra over CC. Recall that there exists an embedding of sl2sl2 into gg, called a principal TDS, passing through a principal nilpotent element of gg and uniquely determined up to conjugation. Moreover, ∧(g⁎)g∧(g⁎)g is freely generated (in the super-graded sense) by primitive elements ω1,…,ωℓω1,…,ωℓ, where ℓ   is the rank of gg. N. Hitchin conjectured that for any primitive element ω∈∧d(g⁎)gω∈∧d(g⁎)g, there exists an irreducible sl2sl2-submodule Vω⊂gVω⊂g of dimension d such that ω   is non-zero on the line ∧d(Vω)∧d(Vω). We prove that the validity of this conjecture for simple simply-laced Lie algebras implies its validity for any simple Lie algebra.Let G be a connected, simply-connected, simple, simply-laced algebraic group and let σ be a diagram automorphism of G with fixed subgroup K  . Then, we show that the restriction map R(G)→R(K)R(G)→R(K) is surjective, where R   denotes the representation ring over ZZ. As a corollary, we show that the restriction map in the singular cohomology H⁎(G)→H⁎(K)H⁎(G)→H⁎(K) is surjective. Our proof of the reduction of Hitchin's conjecture to the simply-laced case relies on this cohomological surjectivity.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 35, Supplement, September 2014, Pages 210–223
نویسندگان
, ,