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arXiv · 1501.04380

The ranks of homotopy groups of Kac-Moody groups

Zhao Xu-an·Jin Chunhua
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Abstract

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 $k>0$.

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Zhao Xu-an, Jin Chunhua. 2015-01-19. The ranks of homotopy groups of Kac-Moody groups. https://arxiv.org/abs/1501.04380

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