Chern character of Schur bundles

Given a vector bundle $E$, we give an explicit formula to compute Chern classes of Schur bundles $\operatorname{S}^αE$ in terms of those of $E$.

💡 Research Summary

The paper “Chern character of Schur bundles” presents a compact and effective method for computing the Chern character (and its twisted variant) of Schur functor bundles S^αE associated to a holomorphic vector bundle E on a compact complex manifold. The authors avoid the cumbersome combinatorics of the classical splitting principle by developing a purely algebraic framework based on symmetric functions and derivations.

The core technical tool is the “Key Lemma” (Lemma 1.3). In this lemma the authors consider the polynomial ring R = ℚ