Prime ideals in the quantum grassmannian
نویسندگان
چکیده
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 G q (m, n) 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 non-negative cells in recent studies concerning the totally non-negative grassmannian. Finally, we use the cell decomposition to establish that the quantum grassmannian satisfies normal separation and catenarity.
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