We prove a characteristic-free plethysm formula of the complex SS2φ for a map of finite free modules φ. We also study a family of subcomplexes of a Schur complex, the v-Schur complexes. Using these machineries from characteristic-free representation theory of general linear group, we give an example of determinantal ideal of generic symmetric matrix whose second Betti number depends on the characteristic of the base field. We also give a short proof of Kurano's first syzygy theorem.
ASJC Scopus subject areas
- Algebra and Number Theory