B. Dynkin in his famous work on the classification of semisimple subalgebras of semisimple Lie algebras in 1952. Dynkin index offers a way to study the different embeddings of a simple subalgebra into a complex simple Lie algebra, and the Dynkin index is also used in the Wess–Zumino–...
研究了Bernstein-Gelfand-Ponomarev反射函子在带自同构σ的箭图Q的F-稳定表示上的作用,并证明了当Q是Dynkin图时,存在一个从Q的不可分解F-稳定表示的同构类到(Q,σ)对应的赋值图的正根的双射。点赞(0) 踩踩(0) 反馈 所需:1 积分 电信网络下载 ...
1) Dynkin index of an irreducible representation . Let [equation] be a finite-dimensional simple complex Lie algebra . The Killing form κ is the invariant bilinear form on [equation]defined by the...Bianchi, MassimoAllen, RolandMondragon, Antonio...
The goal of this note is to prove a closed formula for the Dynkin index of a principal $sl_2$-subalgebra of $g$. The key step in the proof uses the "strange formula" of Freudenthal--de Vries. As an application, we (1) compute the Dynkin index any simple $g$-module regarded as...
In this note, we provide simple formulae for the index of sl 2 sl 2 mathContainer Loading Mathjax -subalgebras in the classical Lie algebras and a new formula for the index of the principal sl 2 sl 2 mathContainer Loading Mathjax . We also compute the difference, D , of the indices...
On the Dynkin index of a principal sl2-subalgebra, ArtículoLet g g mathContainer Loading Mathjax be a simple Lie algebra over an algebraically closed field of characteristic zero. The goal of this note is to prove a closed formula for the Dynkin index of a principal sl 2 sl 2 math...
In this process, we find a new Dynkin index of g2 in e8 with value 4.Lastly, we study the Lie algebra e7?1/2. This Lie algebra comes from P. Deligne's work on the exceptional series of Lie groups. We study the structure of e7?1/2 by realizing it as the derived subalgebra of...
We review two related notions of index introduced by Dynkin, one the index of a subgroup or subalgebra in a semi-simple group or algebra and the other being the index of a linear representation of a semi-simple Lie algebra. Am...
This conjecture has been proven to be true for Dynkin index i = 1 and g = A (1) n , ,C (1) B(1)n ,D (1) n ,A (2) 2n?1 ,A (2) 2n ,D (2) n+1 by Kashiwara, Nakashima and Okado, g = D (3) 4 by Igarashi, Misra and Nakashima, and g = G (1) 2 by ...
A^{(1)}_{n}-Geometric Crystal Corresponding to Dynkin Index i=2 and Its Ultra-Discretizationdoi:10.1007/978-1-4471-4863-0_12Kailash C. MisraToshiki NakashimaSpringer, London