Let \(n\geq 4\), \(2 \leq r \leq n-2\) and \(e \geq 1\). We show that the intersection of the locus of degree \(e\) morphisms from \(\mathbb{P}^1\) to \(G(r,n)\) with the restricted universal sub-bundles having a given splitting type and the locus of degree \(e\) morphisms with the restricted universal quotient-bundle having a given splitting type is non-empty and generically transverse. As a consequence, we get that the locus of degree \(e\) morphisms from \(\mathbb{P}^1\) to \(G(r,n)\) with the restricted tangent bundle having a given splitting type need not always be irreducible.
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