Plücker formulae and Cartan matrices. (English. Russian original) Zbl 0694.14007
Russ. Math. Surv. 44, No. 3, 193-194 (1989); translation from Usp. Mat. Nauk 44, No. 3(267), 155-156 (1989).
The author introduces a conjecture on the integral curves of a certain distribution on the flag manifold of a simple Lie group G. The case \(G=SU_{n+1}\) corresponds to the general Plücker formula [see P. Griffiths and J. Harris: “Principles of algebraic geometry” (1978; Zbl 0408.14001); p. 270]. The case \(G=Sp_{2n}\) leads to the Plücker formula for the autodual curves in \({\mathbb{P}}^{2n-1}\) whose definition uses the symplectic structure on \({\mathbb{C}}^{2n}\).
Reviewer: A.Dimca
MSC:
14H99 | Curves in algebraic geometry |
17B20 | Simple, semisimple, reductive (super)algebras |
51N35 | Questions of classical algebraic geometry |