Algebraic Frobenius Splitting of Cotangent Bundles of Flag Varieties

TL;DR

This paper constructs a Frobenius splitting of the cotangent bundle of flag varieties using representation theory, aligning with previous splittings and advancing understanding in algebraic geometry over positive characteristic fields.

Contribution

It introduces a new representation-theoretic method to construct Frobenius splittings of cotangent bundles of flag varieties, confirming consistency with existing splittings.

Findings

Constructed a Frobenius splitting of cotangent bundles

Demonstrated the splitting matches previous constructions

Enhanced understanding of Frobenius splitting in algebraic geometry

Abstract

Following the program of algebraic Frobenius splitting begun by Kumar and Littelmann, we use representation-theoretic techniques to construct a Frobenius splitting of the cotangent bundle of the flag variety of a semisimple algebraic group over an algebraically closed field of positive characteristic. We also show that this splitting is the same as one of the splittings constructed by Kumar, Lauritzen, and Thomsen.