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

Lookup NU author(s): Dr 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 [T.H. Lenagan, L. Rigal, Quantum graded algebras with a straightening law and the AS–Cohen–Macaulay property for quantum determinantal rings and quantum Grassmannians, 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.

Publication metadata

Author(s): Kolb S

Publication type: Article

Publication status: Published

Journal: Journal of Algebra

Year: 2008

Volume: 319

Issue: 8

Pages: 3518-3534

ISSN (print): 0021-8693

ISSN (electronic): 1090-266X

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.jalgebra.2007.10.004

DOI: 10.1016/j.jalgebra.2007.10.004

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