Boltje-Maisch resolutions of Specht modules
Xingyu Dai, Fang Li, Kefeng Liu
TL;DR
This paper proves the exactness of the Boltje-Maisch complex of Specht modules in the dominant weight case, connecting permutation complexes in Hecke algebra and symmetric group representations.
Contribution
It establishes the exactness of Boltje-Maisch complexes for Specht modules in the dominant weight case, clarifying their role in representation theory.
Findings
Proves exactness of Boltje-Maisch complex in dominant weight case
Links permutation complexes across Hecke algebras and symmetric groups
Enhances understanding of Specht module resolutions
Abstract
In \cite{21}, Boltje and Maisch found a permutation complex of Specht modules in representation theory of Hecke algebras, which is the same as the Boltje-Hartmann complex appeared in the representation theory of symmetric groups and general linear groups. In this paper we prove the exactness of Boltje-Maisch complex in the dominant weight case.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra