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arXiv · 0707.1389

The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weight

Stefan Kolb
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Abstract

It is shown that quantum homogeneous coordinate rings of generalised flag manifolds corresponding to minuscule weights, their Schubert varieties, big cells, and determinantal varieties are AS-Cohen-Macaulay. The main ingredient in the proof is the notion of a quantum graded algebra with a straightening law, introduced by T.H. Lenagan and L. Rigal [J. Algebra 301 (2006), 670-702]. Using Stanley's Theorem it is moreover shown that quantum generalised flag manifolds of minuscule weight and their big cells are AS-Gorenstein.

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Stefan Kolb. 2007-07-10. The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weight. https://arxiv.org/abs/0707.1389

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