Projects per year
Abstract
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 Oq(G(m,n)(k)) and the cell decomposition of the set of Hprimes leads to a parameterisation of the Hspectrum 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.
Original language  English 

Pages (fromto)  697725 
Number of pages  29 
Journal  Selecta Mathematica (New Series) 
Volume  13 
Issue number  4 
DOIs  
Publication status  Published  May 2008 
Keywords
 quantum matrices
 quantum grassmannian
 quantum Schubert variety
 quantum Schubert cell
 prime spectrum
 total positivity
 ALGEBRAS
 RINGS
 DETERMINANTS
 MATRICES
 SPECTRA
 CELLS
Projects
 1 Finished

Prime spectra, automorphism groups and poisson structures associated with quantum algebras
1/03/06 → 28/02/08
Project: Research