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Prime ideals in the quantum grassmanian

Launois, Stephane, Lenagan, T.H., Rigal, L. (2008) Prime ideals in the quantum grassmanian. Selecta Mathematica - New Series, 13 (4). pp. 697-725. ISSN 1022-1824. (doi:10.1007/s00029-008-0054-z) (KAR id:14632)

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We consider quantum Schubert cells in the quantum grassmannian and give a cell decomposition of the prime spectrum via the Schubert cells. As a consequence, we show that all primes are completely prime in the generic case where the deformation parameter q is not a root of unity. There is a natural torus action of H = (k*)(n) on the quantum grassmannian O-q(G(m,n)(k)) and the cell decomposition of the set of H-primes leads to a parameterisation of the H-spectrum via certain diagrams on partitions associated to the Schubert cells. Interestingly, the same parameterisation occurs for the nonnegative cells in recent studies concerning the totally nonnegative grassmannian. Finally, we use the cell decomposition to establish that the quantum grassmannian satisfies normal separation and catenarity.

Item Type: Article
DOI/Identification number: 10.1007/s00029-008-0054-z
Uncontrolled keywords: quantum matrices; quantum grassmannian; quantum Schubert variety; quantum Schubert cell; prime spectrum; total positivity
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Stephane Launois
Date Deposited: 17 Apr 2009 13:25 UTC
Last Modified: 06 May 2020 03:03 UTC
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