We define the notion of a piecewise linear map from a fan \(\Sigma \) to \(\tilde{\mathfrak {B}}(G)\), the cone over the Tits building of a linear algebraic group G. Let \(X_\Sigma \) be a toric variety with fan \(\Sigma \). We show that when G is reductive the set of integral piecewise linear maps from \(\Sigma \) to \(\tilde{\mathfrak {B}}(G)\) classifies the isomorphism classes of (framed) toric principal G-bundles on \(X_\Sigma \). This in particular recovers Klyachko’s classification of toric vector bundles, and gives new classification results for the orthogonal and symplectic toric principal bundles.

我们定义了从扇形\(\Sigma \)到\(\tilde{\mathfrak {B}}(G)\)的分段线性映射的概念，即线性代数群G的 Tits 构建上的圆锥。让\(X_\Sigma \)是一个带有扇形\(\Sigma \)的复曲面变体。我们表明，当G是约简时，从\(\Sigma \)到\(\tilde{\mathfrak {B}}(G)\)的积分分段线性映射集对（框架）复曲面主体G的同构类进行分类- \(X_\Sigma \)上的捆绑包. 这特别恢复了 Klyachko 对复曲面向量丛的分类，并为正交和辛复曲面主丛提供了新的分类结果。