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arXiv · 2503.10461

Exact Borel subalgebras, idempotent quotients and idempotent subalgebras

Teresa Conde·Julian Külshammer
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Abstract

This article studies the compatibility of Koenig's notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide bounds for the multiplicities of indecomposable projectives in the principal blocks of BGG category $\mathcal{O}$ having basic regular exact Borel subalgebras.

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Teresa Conde, Julian Külshammer. 2025-03-13. Exact Borel subalgebras, idempotent quotients and idempotent subalgebras. https://doi.org/10.1007/s00209-026-04005-8

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