JournalsrlmVol. 33, No. 4pp. 925–957

LS algebras, valuations, and Schubert varieties

  • R. Chirivì

    Università del Salento, Lecce, Italy

  • Xin Fang

    Universität zu Köln, Germany

  • Peter Littelmann

    Universität zu Köln, Germany
LS algebras, valuations, and Schubert varieties cover

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Abstract

In this paper, we propose an algebraic approach via Lakshmibai–Seshadri (LS) algebras to establish a link between standard monomial theories, Newton–Okounkov bodies and valuations. This is applied to Schubert varieties, where this approach is compatible with the one using Seshadri stratifications in arXiv:2112.03776, showing that LS paths encode vanishing multiplicities with respect to the web of Schubert varieties.

Cite this article

R. Chirivì, Xin Fang, Peter Littelmann, LS algebras, valuations, and Schubert varieties. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 4, pp. 925–957

DOI 10.4171/RLM/993