Standard monomial theory modulo Frobenius in characteristic two

Laura Casabella; Teresa Yu

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arXiv · 2311.05530

Standard monomial theory modulo Frobenius in characteristic two

Laura Casabella·Teresa Yu

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Abstract

Over a field of characteristic two, we develop a theory of standard monomials for polynomial rings modulo a Frobenius power of the maximal ideal generated by all variables. As a result, we obtain a filtration by modular GL_n-representations whose characters are given by particular truncated Schur polynomials, thus proving a conjecture by Gao--Raicu--VandeBogert in the characteristic two case.

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Laura Casabella, Teresa Yu. 2023-11-09. Standard monomial theory modulo Frobenius in characteristic two. https://arxiv.org/abs/2311.05530

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