arXiv subjects

Jin Chunhua

Publications and source records attributed to Jin Chunhua.

3 recordsLinked to original sources

arXiv2015

The ranks of homotopy groups of Kac-Moody groups

Let $A$ be a Cartan matrix and $G(A)$ be the Kac-Moody group associated to Cartan matrix $A$. In this paper, we discuss the computation of the rank $i_k$ of homotopy group $π_k(G(A))$. For a large class of Kac-Moody groups, we construct Lie algebras with grade from the Poincaré series of their flag manifolds. And we interpret $i_{2k}$ as the dimension of the degree $2k$ homogeneous component of the Lie algebra we constructed. Since the computation of $i_{2k-1}$ is trivial, this gives a combinatorics interpretation of $i_k$ for all $k>0$.

math.AT↗

arXiv2013

Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds

In this paper, we study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds. By extracting the information of cohomology from the Poincaré series, we are able to determine the rational cohomology rings of Kac-Moody groups and their flag manifolds. Since Kac-Moody groups and their flag manifolds are rational formal, we also determine their rational homotopy groups and rational homotopy types.

math.AT↗

arXiv2012

Polynomial invariants of Weyl groups for Kac-Moody groups

In this paper, we prove that the ring of polynomial invariants of the Weyl group for an indecomposable and indefinite Kac-Moody Lie algebra is generated by invariant symmetric bilinear form or is trivial depending on $A$ is symmetrizable or not. The result was conjectured by Moody and assumed by Kac. As applications we discuss the rational homotopy types of Kac-Moody groups and their flag manifolds.

math.AC↗